PUBLICATIONS

by Mark M. Meerschaert

  1. J.F. Kelly, C.G. Li and M.M. Meerschaert, Anomalous Diffusion with Ballistic Scaling: A New Fractional Derivative, Journal of Computational and Applied Mathematics, Vol. 339 (2018), pp. 161178.  Special Issue on Modern fractional dynamic systems and applications.
  2. B. Baeumer, M. Kovács, M.M. Meerschaert, and H. Sankaranarayanan, Reprint of: Boundary Conditions for Fractional Diffusion, Journal of Computational and Applied Mathematics, Vol. 339 (2018), pp. 414–430.
  3. P. Kern, M.M. Meerschaert, and Y. Xiao, Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties, Journal of Theoretical Probability,  Vol. 31 (2018), No. 1, pp. 598617.
  4. B. Baeumer, M. Kovács, M.M. Meerschaert, and H. Sankaranarayanan, Boundary Conditions for Fractional Diffusion, Journal of Computational and Applied Mathematics, Vol. 336 (2018), pp. 408–424.  Special Issue on Modern fractional dynamic systems and applications. Click here to download the R codes for this paper. 
  5. G. Didier, M.M. Meerschaert, and V. Pipiras, Domain and range symmetries of operator fractional Brownian fields, Stochastic Processes and their Applications, Vol. 128 (2018), No. 1, pp. 39–78. 
  6. J.F. Kelly and M.M. Meerschaert, Space-time duality for the fractional advection dispersion equation, Water Resources Research, Vol. 53 (2017), No. 4, pp. 3464–3475.
  7. J.F. Kelly, D. Bolster, M.M. Meerschaert, J.D. Drummond, and A.I. Packman, FracFit: A Robust Parameter Estimation Tool for Fractional Calculus Models, Water Resources Research,  Vol. 53 (2017), No. 3, pp. 1763–2576.
  8. M.S. Alrawashdeh, J,F. Kelly, M.M. Meerschaert, and H.-P. Scheffler, Applications of Inverse Tempered Stable Subordinators, Computers and Mathematics with Applications,  Vol. 73 (2017), No. 6, pp. 892–905. DOI: 10.1016/j.camwa.2016.07.026.  Special Issue on Time-fractional PDEs. 
  9. G. Didier, M.M. Meerschaert, and V. Pipiras, Exponents of operator self-similar random fields, Journal of Mathematical Analysis and Applications,  Vol. 448 (2017), No. 2, pp. 1450–1466.
  10. M.M. Meerschaert and Farzad Sabzikar, Tempered fractional stable motion, Journal of Theoretical Probability, Vol. 29 (2016), No. 2, pp. 681–706, DOI 10.1007/s10959-014-0585-5.
  11. Y. Zhang, M.M. Meerschaert, and R.M. Neupauer, Backward fractional advection dispersion model for contaminant source prediction, Water Resources Research, Vol. 52 (2016), No. 4, pp. 2462–2473, doi:10.1002/2015WR018515.
  12. M.M. Meerschaert, R.L. Magin, and A.Q. Ye, Anisotropic fractional diffusion tensor imaging, Journal of Vibration and Control, Vol. 22 (2016), No. 9, pp. 2211–2221. Special Issue on Challenges in Fractional Dynamics and Control Theory.
  13. B. Baeumer, M. Kovács, M.M. Meerschaert, R.L. Schilling, and P. Straka, Reflected spectrally negative stable processes and their governing equations, Transactions of the American Mathematical Society, Vol. 368 (2016), No. 1, pp. 227–248.
  14. Y. Zhang, M.M. Meerschaert, B. Baeumer, and E.M. LaBolle,  Modeling mixed retention and early arrivals in multi-dimensional heterogeneous media using an explicit Lagrangian scheme, Water Resources Research, Vol. 51 (2015), pp. 6311–6337, doi:10.1002/2015WR016902.
  15. M.M. Meerschaert, R.L. Schilling, and A. Sikorskii, Stochastic solutions for fractional wave equations, Nonlinear Dynamics, Vol. 80 (2015), No. 4, pp. 1685–1695, Special issue on Fractional Dynamics and Its Applications.
  16. F. Sabzikar, M.M. Meerschaert, and J. Chen, Tempered Fractional Calculus, Journal of Computational Physics, Vol. 293 (2015), pp. 14–28, Special Issue on Fractional Partial Differential Equations.  Winner of the Riemann-Liouville Award for the Best Theory Paper at the International Symposium on Fractional Differentiation and Its Applications, Catania, Sicily, Italy, June 2014.
  17. O. Defterli, M. D’Elia, Q. Du, M. Gunzburger, R. Lehoucq, and M.M. Meerschaert, Fractional diffusion on bounded domains, Fractional Calculus and Applied Analysis, Vol. 18 (2015), No. 2, pp. 342–360.
  18. Mine Dogan, Remke L. Van Dam, Gaisheng Liu, Mark M. Meerschaert, James J. Butler Jr., Geoffrey C. Bohling, David A. Benson, and David W. Hyndman, Predicting flow and transport in highly heterogeneous alluvial aquifers, Geophysical Research Letters, Vol. 41 (2014), No. 21, pp. 7560–7565, 10.1002/2014GL061800. 
  19. N.N. Leonenko, M.M. Meerschaert, R.L. Schilling, and A. Sikorskii, Correlation Structure of Time-Changed Lévy Processes, Communications in Applied and Industrial Mathematics, Vol. 6 (2014), No. 1, p. e-483 (22 pp.),  DOI: 10.1685/journal.caim.483, Special Issue in Honor of Francesco Mainardi.
  20. M.M. Meerschaert, Farzad Sabzikar, M.S. Phanikumar, and A. Zeleke, Tempered fractional time series model for turbulence in geophysical flows, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014 p. P09023 (13 pp.) doi:10.1088/1742-5468/2014/09/P09023.
  21. M.M. Meerschaert and R.J. McGough, Attenuated fractional wave equations with anisotropy, Journal of Vibration and Acoustics, Vol. 36 (2014), No. 5, 051004 (5 pp.),  doi: 10.1115/1.4025940.
  22. M.M. Meerschaert and P. Straka, Semi-Markov approach to continuous time random walk limit processes, The Annals of Probability, Vol. 42 (2014), No. 4, pp. 1699–1723.  Conference talk on this paper with additional details and figures.
  23. M.M. Meerschaert and Farzad Sabzikar, Stochastic integration for tempered fractional Brownian motion, Stochastic Processes and their Applications,  Vol. 124 (2014), No. 7, pp. 2363–2387. One of the top 25 hottest articles in this journal from April to June 2014.
  24. C.Y. Lim, M.M. Meerschaert, and H.-P. Scheffler, Parameter estimation for operator scaling random fields, Journal of Multivariate Analysis, Vol. 123 (2014), pp. 172–183, DOI: 10.1016/j.jmva.2013.09.010.
  25. M.M. Meerschaert, H.-P. Scheffler, and S. Stoev, Extreme value theory with operator norming, Extremes, Vol. 16 (2013), No. 4, pp. 407–428.
  26. J.J. GadElkarim, R.L.Magin, M.M. Meerschaert, S. Capuani, M. Palombo, A. Kumar, and A.D. Leow, Fractional order generalization of anomalous diffusion as a multidimensional extension of the transmission line equation, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, Vol. 3 (2013), No. 3, pp. 432–441, DOI: 0.1109/JETCAS.2013.2265795.
  27. M.M. Meerschaert, M. Dogan, R.L. Van Dam, D.W. Hyndman, and D.A. Benson, Hydraulic Conductivity Fields: Gaussian or Not? Water Resources Research, Vol. 49 (2013), pp. 4730–4737, doi:10.1002/wrcr.20376
  28. H. Zhang, F. Liu, M.S. Phanikumar, and M.M. Meerschaert, A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model, Computers & Mathematics with Applications, Vol. 66 (2013), No. 5, pp, 693–701.
  29. N.N. Leonenko, M.M. Meerschaert, and A. Sikorskii, Correlation Structure of Fractional Pearson Diffusions, Computers and Mathematics with Applications, Vol. 66 (2013), No. 5, pp. 737–745.
  30. M.M. Meerschaert and Farzad Sabzikar, Tempered Fractional Brownian Motion, Statistics and Probability Letters, Vol. 83 (2013), No. 10, pp. 2269–2275.
  31. M.M. Meerschaert and P. Straka,  Inverse stable subordinators, Mathematical Modeling of Natural Phenomena, Vol. 8 (2013), No. 2, pp. 1–16.  Click here to download R codes used in this paper.
  32. N.N. Leonenko, M.M. Meerschaert, and A. Sikorskii, Fractional Pearson diffusions, Journal of Mathematical Analysis and Applications, Vol. 403 (2013), No. 2, pp. 532–546.
  33. D. Bolster, D.A. Benson, M.M. Meerschaert and B. Baeumer, Mixing-driven equilibrium reactions in multidimensional fractional advection dispersion systems, Physica A: Statistical Mechanics and its Applications, Vol. 392 (2013), No. 10, pp. 2513–2525.
  34. M.M. Meerschaert and H.-P. Scheffler, Tauberian theorems for matrix regular variation, Transactions of the American Mathematical Society, Vol. 365 (2013), No. 4, pp. 2207–2221.
  35. P.L. Anderson, M.M. Meerschaert, and K. Zhang, Forecasting for periodic ARMA models, Journal of Time Series Analysis, Vol. 34 (2013), No. 2, pp.187–193.  Click here for the R codes to accompany this paper. 
  36. M.M. Meerschaert, E. Nane; and P. Vellaisamy, Transient anomalous sub-diffusion on bounded domains, Proceedings of the American Mathematical Society, Vol. 141 (2013), No. 2,  pp. 699–710.
  37. M.M. Meerschaert, W. Wang, and Y. Xiao, Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields, Transactions of the American Mathematical Society, Vol. 365 (2013), No. 2, pp. 1081–1107.
  38. M.M. Meerschaert, Mathematical Modeling, 4th Edition (2013), Academic Press, ISBN 978-0-12-386912-8.
  39. M.M. Meerschaert, E. Nane and Y. Xiao, Fractal dimensions for continuous time random walk limits, Statistics and Probability Letters, Vol. 83 (2013), No. 4, pp. 1083–1093.
  40. H. Sun, M.M. Meerschaert, Y. Zhang, J. Zhu, and W. Chen, A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media, Advances in Water Resources, Vol. 52 (2013), pp.292–295.
  41. D.A. Benson, M.M. Meerschaert, and J. Revielle, Fractional calculus in hydrologic modeling: A numerical perspective, Advances in Water Resources, Vol. 51 (2013), pp. 479–497, doi:10.1016/j.advwatres.2012.04.005.
  42. F. Liu, M.M. Meerschaert, R.J. McGough, P. Zhuang, and Q. Liu, Numerical methods for solving the multi-term time-fractional wave-diffusion equations, Fractional Calculus and Applied Analysis, Vol. 16 (2013), No 1, pp. 9–25, DOI: 10.2478/s13540-013-0002-2.
  43. P. Straka, M.M. Meerschaert, R.J. McGough, and Y. Zhou,  Fractional wave equations with attenuation, Fractional Calculus and Applied Analysis, Vol. 16 (2013), No 1, pp. 262–272, DOI: 10.2478/s13540-013-0016-9
  44. H. Jiang, F. Liu, M.M. Meerschaert, R.J. McGough, and Q. Liu, The fundamental solutions for multi-term modified power law wave equations in a finite domain, Electronic Journal of Mathematical Analysis and Applications, Vol. 1 (2013), No. 7, pp. 1–12.
  45. M.M. Meerschaert and P. Straka, Fractional dynamics at multiple times, Journal of Statistical Physics, Vol. 149 (2012), pp. 878–886.  Click here to download R codes used in this paper.
  46. Y. Zhang, M.M. Meerschaert, and A.I. Packman, Linking fluvial bed sediment transport across scales, Geophysical Research Letters, Vol. 39 (2012), L20404 (6 pp.), doi:10.1029/2012GL053476.
  47. A. Jurlewicz, P. Kern, M.M. Meerschaert, and H.-P. Scheffler, Fractional governing equations for coupled random walks, Computers and Mathematics with Applications, Vol.64 (2012), pp. 3021–3036. Special Issue on Advances in Fractional Differential Equations III.  Click here to download R codes used in this paper.
  48. M.M. Meerschaert, P. Straka, Y. Zhou, and R.J. McGough, Stochastic solution to a time-fractional attenuated wave equation, Nonlinear Dynamics, Vol. 70 (2012), No. 2, pp. 1273–1281.
  49. D. Bolster, M.M. Meerschaert, and A. Sikorskii, Product rule for vector fractional derivatives, Fractional Calculus and Applied Analysis, Vol. 15 (2012), No. 3, pp. 463–478.
  50. K.Weron, A. Stanislavsky, A. Jurlewicz, M.M. Meerschaert, and H.-P. Scheffler, Clustered continuous time random walks: Diffusion and relaxation consequences, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 468 (2012), No. 2141, pp. 1615–1628, doi:10.1098/rspa.2011.0697.
  51. Z.Q. Chen, M.M. Meerschaert, and E. Nane, Space-time fractional diffusion on bounded domains, Journal of Mathematical Analysis and Applications, Vol. 393 (2012), No. 2, pp.479–488, doi:10.1016/j.jmaa.2012.04.032.
  52. M.M. Meerschaert, P. Roy, and Q. Shao, Parameter estimation for tempered power law distributions, Communications in Statistics – Theory and Methods, Vol. 41 (2012), No. 10, pp. 1839–1856. Click here to download R codes and data sets used in this paper.
  53. M.M. Meerschaert and Alla Sikorskii, Stochastic Models for Fractional Calculus, De Gruyter Studies in Mathematics Vol. 43, 2012, ISBN 978-3-11-025869-1.
  54. M.M. Meerschaert, Fractional Calculus, Anomalous Diffusion, and Probability, Fractional Dynamics, R. Metzler and J. Klafter, Eds., World Scientific, Singapore, pp. 265--284, 2012.
  55. A. Jurlewicz, M.M. Meerschaert, and H.P. Scheffler, Cluster continuous time random walks, Studia Mathematica, Vol. 205 (2011), No. 1, pp.13--30.
  56. M.M. Meerschaert, E. Nane, and P. Vellaisamy, The fractional Poisson process and the inverse stable subordinator, Electronic Journal of Probability, Vol. 16 (2011), Paper no. 59, pp. 1600–1620.
  57. Yong Zhang and M. M. Meerschaert, Gaussian setting time for solute transport in fluvial systems, Water Resources Research, Vol. 47 (2011), W08601, doi:10.1029/2010WR010102.
  58. A. Chakrabarty and M. M. Meerschaert,  Tempered stable laws as random walk limits, Statistics and Probability Letters, Vol. 81 (2011), No. 8, pp. 989-997. 
  59. Y.G. Tesfaye, P.L. Anderson, and M.M. Meerschaert, Asymptotic results for Fourier-PARMA time series, Journal of Time Series Analysis, Vol. 32 (2011), No. 2, pp. 157-174.
  60. M.M. Meerschaert, E. Nane, and P. Vellaisamy, Distributed-order fractional Cauchy problems on bounded domains, Journal of Mathematical Analysis and Applications, Vol. 379 (2011), pp. 216–228.
  61. R. Schumer, B. Baeumer, and M. M. Meerschaert, Extremal behavior of a coupled continuous time random walk, Physica A: Statistical Mechanics and Its Applications, Vol. 390 (2011), pp. 505–511.
  62. A. Kumar, M.M. Meerschaert, and P. Vellaisamy, Fractional Normal Inverse Gaussian Diffusion, Statistics and Probability Letters, Vol. 81 (2011) pp. 146–152.
  63. S. Cohen, M. M. Meerschaert and J. Rosiński, Modeling and simulation with operator scaling, Stochastic Processes and Their Applications, Vol.120 (2010) pp. 2390–2411.  Click here for an extended version with additional examples and details.  Click here to download MAPLE software used to compute the model parameters, and here for MATLAB software to implement the sample path simulations.
  64. B. Baeumer, M. M. Meerschaert and M. Naber, Stochastic models for relativistic diffusion, Physical Review E,  Vol. 82 (2010), pp. 011132.
  65. K. M. Hill, L. DellAngelo, and M. M. Meerschaert, Heavy tailed travel distance in gravel bed transport: An exploratory enquiry, Journal of Geophysical Research, Vol. 115 (2010), p. F00A14, doi:10.1029/2009JF001276.
  66.  V. Ganti, M. M. Meerschaert, E. Foufoula-Georgiou, E. Viparelli, and G. Parker, Normal and Anomalous Dispersion of Gravel Tracer Particles in Rivers, Journal of Geophysical Research, Vol. 115 (2010), p. F00A12, doi:10.1029/2008JF001222.
  67. V. R. Vásquez, W. B. Whiting, and M. M. Meerschaert, Confidence interval estimation under the presence of non-Gaussian random errors: applications to uncertainty analysis of chemical processes and simulation, Computers & Chemical Engineering, Vol. 34 (2010), pp. 298–305, doi:10.1016/j.compchemeng.2009.11.004.
  68. B. Baeumer and M. M. Meerschaert, Tempered stable Levy motion and transient super-diffusion, Journal of Computational and Applied Mathematics, Vol. 233 (2010), pp. 2438-2448, 10.1016/j.cam.2009.10.027.
  69. M. M. Meerschaert, Y. Zhang, and B. Baeumer Particle tracking for fractional diffusion with two time scales, Computers and Mathematics with Applications, Special Issue on Advances in Fractional Differential Equations, Vol. 59 (2010), No. 3, pp. 1078-1086, doi:10.1016/j.camwa.2009.05.009.
  70.  B. Baeumer, M.M. Meerschaert and E. Nane, Space-time duality for fractional diffusion, Journal of Applied Probability, Vol. 46 (2009), pp. 1100-1115.
  71. R. Schumer, M. M. Meerschaert, and B. Baeumer, Fractional advection-dispersion equations for modeling transport at the Earth surface, Journal of Geophysical Research, Vol. 114 (2009), p. F00A07, doi:10.1029/2008JF001246. 
  72. P. Chakraborty, M. M. Meerschaert, and C. Y. Lim, Parameter Estimation for Fractional Transport: A particle tracking approachWater Resources Research, Vol. 45 (2009), W10415, doi:10.1029/2008WR007577.
  73. Bill X. Hu, Mark M. Meerschaert, Warren Barrash, David W. Hyndman, Changming He, Xinya Li, and Luanjing Guo, Examining the Influence of Heterogeneous Porosity Fields on Conservative Solute Transport, Journal of Contaminant Hydrology, Vol. 108 (2009), Issues 3-4, pp. 77–88, doi:10.1016/j.jconhyd.2009.06.001.
  74. T.J. Kozubowski, M.M. Meerschaert, A bivariate infinitely divisible distribution with exponential and Mittag-Leffler marginals, Statistics and Probability Letters, Vol. 79 (2009), pp. 1596-1601.
  75. M.M. Meerschaert, E. Nane, P. Vellaisamy, Fractional Cauchy problems on bounded domains, The Annals of Probability, Vol. 37 (2009), No. 3, pp. 979–1007.  Click here to read the accompanying "Members' Discovery" article from the July 2009 IMS Bulletin. 
  76. M.M. Meerschaert, E. Nane, Y. Xiao, Correlated continuous time random walks, Statistics and Probability Letters, Vol. 79 (2009), pp. 1194-1202.
  77.  B. Baeumer, M.M. Meerschaert, E. Nane, Brownian subordinators and fractional Cauchy problems, Transactions of the American Mathematical Society, Vol. 361 (2009), No. 7, pp. 3915–3930. 
  78.  D.A. Benson, M.M. Meerschaert, A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations, Advances in Water Resources, Vol. 32 (2009), pp. 532–539.
  79. M.M. Meerschaert, S. Stoev, Extremal limit theorems for observations separated by random power law waiting times, Journal of Statistical Planning and Inference, Vol.139 (2009), pp. 2175-2188.
  80. H. Guo, C.Y. Lim, M.M. Meerschaert, Local Whittle estimator for anisotropic random fields, Journal of Multivariate Analysis, Vol. 100 (2009), No. 5, pp. 993-1028, doi:10.1016/j.jmva.2008.10.002.
  81. D.A. Benson, M.M. Meerschaert, Simulation of chemical reaction via particle tracking: diffusion-limited versus thermodynamic rate-limited regimes, Water Resources Research, Vol. 44 (2008), p. W12201, doi:10.1029/2008WR007111.
  82. J.F. Kelly and R.J. McGough, M.M. Meerschaert, Analytical time-domain Green’s functions for  power-law media, Journal of the Acoustical Society of America, Vol. 124 (2008) No. 5, pp. 2861–2872.
  83. B. Baeumer, M. Kovács, M.M. Meerschaert, Subordinated multiparameter groups of linear operators: Properties via the transference principle, Functional Analysis and Evolution Equations.  The Günter Lumer Volume. Edited by H. Amann, W. Arendt, M. Hieber,  F. Neubrander, S. Nicaise and J. von Below. Birkhäuser Basel, ISBN 978-3-7643-7793-9, (2008) pp. 35-50.
  84. Y. Zhang, M.M. Meerschaert, B. Baeumer, Particle tracking for time-fractional diffusion, Physical Review E, Vol.78 (2008), No.3, p. 036705 (7 pp.), DOI: 10.1103/PhysRevE.78.036705
  85. M.M. Meerschaert, S.W. Wheatcraft, Fractional Conservation of Mass, Advances in Water Resources, Vol. 31 (2008), pp. 1377–1381.
  86. M.M. Meerschaert, Y. Zhang, B. Baeumer, Tempered anomalous diffusion in heterogeneous systems, Geophysical Research Letters, Vol. 35 (2008), p. L17403, doi:10.1029/2008GL034899.
  87. M.M. Meerschaert, D. Wu, and Y. Xiao, Local Times of Multifractional Brownian Sheets, Bernoulli, Vol. 14 (2008), No. 3, pp. 865–898, DOI: 10.3150/08-BEJ126.
  88. D.M. Reeves, D.A. Benson, M.M. Meerschaert, Influence of Fracture Statistics on Advective Transport and Implications for Geologic Repositories, Water Resources Research, Vol. 44 (2008), W08405, doi:10.1029/2007WR006179.
  89. M.M. Meerschaert, H.P. Scheffler, Triangular array limits for continuous time random walks, Stochastic Processes and their Applications, Vol. 118 (2008), No. 9, pp. 1606–1633. Errata
  90. M.M. Meerschaert, E. Nane, and Y. Xiao, Large deviations for local time fractional Brownian motion and applications, Journal of Mathematical Analysis and Applications, Vol. 346 (2008), pp. 432–445.
  91. D.M. Reeves, D.A. Benson, M.M. Meerschaert, H.P. Scheffler, Transport of Conservative Solutes in Simulated Fracture Networks 2. Ensemble Solute Transport and the Correspondence to Operator-Stable Limit Distributions, Water Resources Research, Vol. 44 (2008), W05410, doi:10.1029/2008WR006858.
  92. D.M. Reeves, D.A. Benson, M.M. Meerschaert, Transport of Conservative Solutes in Simulated Fracture Networks 1. Synthetic Data Generation, Water Resources Research, Vol. 44 (2008), W05404, doi:10.1029/2007WR006069
  93. B. Baeumer, M. Kovács, M.M. Meerschaert, Numerical solutions for fractional reaction-diffusion equations, Computers and Mathematics with Applications, Vol. 55 (2008), pp. 2212–2226.
  94. N.D. Monnig, D.A. Benson, M.M. Meerschaert, Ensemble Solute Transport in 2-D Operator-Scaling Random Fields, Water Resources Research, Vol. 44 (2008), W02434, doi:10.1029/2007WR005998.
  95. T.J. Kozubowski, M.M. Meerschaert, G. Gustafson, A new stochastic model for fracture transmissivity assessment, Water Resources Research, Vol. 44 (2008), p. W02435, doi:10.1029/2007WR006053.
  96. P. L. Anderson, L. Kavalieris, M.M. Meerschaert, Innovations Algorithm Asymptotics for Periodically Stationary Time Series with Heavy Tails, Journal of Multivariate Analysis, Vol. 99 (2008), No. 1, pp. 94-116, DOI 10.1016/j.jmva.2007.02.005.
  97. B. Baeumer, M. Kovács, M.M. Meerschaert, Fractional reproduction-dispersal equations and heavy tail dispersal kernels, Bulletin of Mathematical Biology, Vol. 69 (2007), pp. 2281-2297.
  98. D.A. Benson, R. Schumer, M.M. Meerschaert, Extreme events with power law interarrivals, Geophysical Research Letters, Vol. 34 (2007), No. 16, L16404.
  99. P.L. Anderson, M.M. Meerschaert, Y.G. Tesfaye, Fourier-PARMA Models and Their Application to Modeling of River  Flows, Journal of Hydrologic Engineering, Vol. 12 (2007), No. 5, pp. 462-472.
  100. M.M. Meerschaert, Mathematical Modeling , 3rd Edition, Academic Press, 2007, ISBN 978-0-12-370857-1.
  101. Y. Zhang, D.A. Benson, M.M. Meerschaert, E. M. LaBolle, Space-fractional advection-dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the MADE-site data,  Water Resources Research, Vol. 43 (2007), p. W05439, doi:10.1029/2006WR004912.
  102. H. Biermé, M.M. Meerschaert, H.P. Scheffler, Operator Scaling Stable Random Fields, Stochastic Processes and their Applications, Vol. 117 (2007), pp. 312–332.
  103. C. Tadjeran, M.M. Meerschaert, A second order accurate numerical method for the two-dimensional fractional diffusion equation, Journal of Computational Physics, Vol. 220 (2007) pp. 813–823.  Click here to download the FORTRAN source code used in Section 5 of this paper to implement the Crank-Nicholson alternating directions implicit method with interpolation scheme.
  104. B. Baeumer, M.M. Meerschaert, Fractional diffusion with two time scales, Physica A: Statistical Mechanics and Its Applications, Vol. 373 (2007), pp. 237–251
  105. M. Kovács, M.M. Meerschaert, Ultrafast subordinators and their hitting times, Publications de l'Institut Mathematique, Nouvelle série, Vol. 80(94) (2006), 193–206; Memorial volume for Tatjana Ostrogorski.
  106. T.J. Kozubowski, M.M. Meerschaert, K. Podgórski, Fractional Laplace Motion, Advances in Applied Probability, Vol. 38 (2006), No. 2, pp. 451-464.
  107. Y. Zhang, D.A. Benson, M.M. Meerschaert, E. M. LaBolle, and H.P. Scheffler, Random walk approximation of fractional-order multiscaling anomalous diffusion, Physical Review E, Vol. 74 (2006), 026706 (10 pp).
  108. M.M. Meerschaert, E. Scalas, Coupled continuous time random walks in finance, Physica A: Statistical Mechanics and Its Applications, Vol. 370 (2006), pp. 114-118.
  109. Y. Zhang, D.A. Benson, M.M. Meerschaert, E. M. LaBolle, and H.P. Scheffler, Lagrangian characterization of contaminant transport through multidimensional heterogeneous media with limited heterogeneity informationConference Proceedings for MODFLOW and MORE 2006: Managing Ground-Water Systems, International Ground Water Modeling Center, pp. 639-643.
  110. M.M. Meerschaert, H.P. Scheffler, Stochastic model for ultraslow diffusion, Stochastic Processes and Their Applications, Vol. 116 (2006), No. 9, pp. 1215-1235.
  111.  M.M. Meerschaert, J. Mortensen, and S.W. Wheatcraft, Fractional vector calculus for fractional advection-dispersion, Physica A: Statistical Mechanics and Its Applications, Vol. 367 (2006), pp. 181-190.
  112. Y. Zhang, D.A. Benson, M.M. Meerschaert, H.P. Scheffler, On using random walks to solve the space-fractional advection-dispersion equations, Journal of Statistical Physics, Vol. 123 (2006), No.1, pp. 89-110. 
  113. M. Kohlbecker, S.W. Wheatcraft and M.M. Meerschaert, Heavy tailed log hydraulic conductivity distributions imply heavy tailed log velocity distributions (10.2 MB), Water Resources Research, Vol. 42 (2006), No. 4, article W04411 (12 pp.), doi:10.1029/2004WR003815.
  114. I.B. Aban, M.M. Meerschaert, and A.K. Panorska, Parameter Estimation for the Truncated Pareto Distribution, Journal of the American Statistical Association: Theory and Methods, Volume 101 (2006), Number 473, pp.270-277.  Winner of the 2007 best paper award for a University of Alabama at Birmingham Based Investigator in the Area of General Statistics, from the Science Unbound Foundation.  Click here to download the Microsoft Excel spreadsheet  tool for computing the trauncated Pareto parameter conditional maximum likelihood estimator from this paper.  
  115. C. Tadjeran, M.M. Meerschaert, H.P. Scheffler, A second order accurate numerical approximation for the fractional diffusion equation, Journal of Computational Physics, Vol. 213 (2006), No. 1, pp. 205-213.  Click here to download the FORTRAN source code used in Section 5 of this paper to implement the Crank-Nicholson method and interpolation scheme.
  116. Y.G. Tesfaye, M.M. Meerschaert, and Paul L. Anderson, Identification of PARMA Models and Their Application to the Modeling of Riverflows, Water Resources Research, Vol. 42 (2006), No. 1, W01419 (11pp.), doi:10.1029/2004WR003772.
  117. D.A. Benson, M.M. Meerschaert, B. Baeumer, H.P. Scheffler, Aquifer Operator-Scaling and the Effect on Solute Mixing and Dispersion, Water Resources Research, Vol. 42 (2006), No. 1, W01415 (18 pp.), doi:10.1029/2004WR003755.
  118. M.M. Meerschaert and C. Tadjeran, Finite difference approximations for two-sided space-fractional partial differential equations, Applied Numerical Mathematics, Vol. 56 (2006), No. 1, pp. 80-90.  Click here to download the FORTRAN source code used in Section 4 of this paper to implement the implicit Euler method for a two-sided fractional Fokker-Planck equation.
  119. M.M. Meerschaert, H.P. Scheffler and C. Tadjeran, Finite difference methods for two-dimensional fractional dispersion equation, Journal of Computational Physics, Vol. 211 (2006), No. 1, pp. 249-261.  Click here to download the FORTRAN source code used in Section 4 of this paper to implement the implicit Euler ADI method. 
  120. B. Baeumer, M.M. Meerschaert, and S. Kurita, Inhomogeneous fractional diffusion equations, Fractional Calculus and Applied Analysis, Vol. 8, No 4 (2005), pp. 371-386.
  121. E. Scalas, R. Gorenflo, F. Mainardi, and M.M. Meerschaert, Speculative option valuation and the fractional diffusion equation, Fractional derivatives and their applications, pp. 265-274, A. Le Mehauté, J. A. Tenreiro Machado, J. C. Trigeassou and J. Sabatier, Eds. (2005), Ubooks, Germany, ISBN 3-86608-026-3.
  122. F.J. Molz, M.M. Meerschaert, T.J. Kozubowski and P.D. Hyden,  Do heterogeneous sediment properties and turbulent velocity fluctuations have something in common?  Some history and a new stochastic process.  pp. 13-22,  Dynamics of Fluids and Transport in Fractured Rock. B. Faybishenko, P.A.Witherspoon, and J. Gale, Editors. Geophysical Monograph Series, Volume 162, 250 pages, hardbound, 2005, ISBN 0-87590-427-0.
  123. P.L. Anderson and M.M. Meerschaert,  Parameter estimation for periodically stationary time series, Journal of Time Series Analysis, Vol. 26 (2005), No. 4, pp. 489-518.
  124. D.D. Clarke, M.M. Meerschaert and S.W. Wheatcraft, Fractal Travel Time Estimates for Dispersive Contaminants, Ground Water, Vol. 43 (2005), No. 3, pp. 401-407.
  125. B. Baeumer, M.M. Meerschaert, J. Mortensen, Space-time fractional derivative operators, Proceedings of the American Mathematical Society, Vol. 133 (2005), No. 8, pp. 2273–2282.
  126. B. Baeumer, D.A. Benson, M.M. Meerschaert, Advection and dispersion in time and space, Physica A: Statistical Mechanics and Its Applications, Vol. 350 (2005), No. 2-4, pp. 245-262.
  127. M.M. Meerschaert and H.P. Scheffler, Limit theorems for continuous time random walks with slowly varying waiting times, Statistics and Probability Letters, Vol. 71 (2005), No. 1, pp.15-22.
  128. T.J. Kozubowski, M.M. Meerschaert, A.K. Panorska and H.P. Scheffler, Operator geometric stable laws, Journal of Multivariate Analysis, Vol. 92 (2005) pp. 298-323.
  129. M.M. Meerschaert and Y. Xiao, Dimension results for sample paths of operator stable Levy processes, Stochastic Processes and Their Applications Vol. 115 (2005), No. 1, pp. 55-75.
  130. D.A. Benson, C. Tadjeran, M.M. Meerschaert, I. Farnham, and G. Pohll, Radial Fractional–Order Dispersion Through Fractured Rock, Water Resources Research, Vol. 40 (2004), No. 12, pp. 1-9, doi:10.1029/2004WR003314.
  131. M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations Journal of Computational and Applied Mathematics, Vol. 172 (2004), No. 1, pp. 65-77.  Click here to download the FORTRAN source code as well as a sample terminal session used in section 3 of this paper to implement the implicit Euler method to solve the space-fractional radial flow equation.
  132. M.M. Meerschaert and H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times Journal of Applied Probability, Vol 41 (2004), No. 3, pp. 623-638.
  133. M.M. Meerschaert, J. Mortensen and H.P. Scheffler, Vector Grünwald formula for fractional derivatives Fractional Calculus and Applied Analysis, Vol. 7 (2004), No. 1, pp. 61-81.
  134. P. Becker-Kern, M.M. Meerschaert and H.P. Scheffler, Limit theorem for continuous time random walks with two time scales, Journal of Applied Probability, Vol. 41 (2004), pp. 455-466.
  135. M.M. Meerschaert, T.J. Kozubowski, F.J. Molz, and S. Lu, Fractional Laplace Model for Hydraulic Conductivity Geophysical Research Letters, Vol. 31, No. 8 (2004), pp. 1-4, doi:10.1029/2003GL019320.
  136. I.B. Aban and M.M. Meerschaert, Generalized least squares estimators for the thickness of heavy tails, Journal of Statistical Planning and Inference, Vol. 119 (2004), pp. 341-352.
  137.  P. Becker-Kern, M.M. Meerschaert and H.P. Scheffler, Limit theorems for coupled continuous time random walks, The Annals of Probability, Vol. 32 (2004), No. 1B, pp. 730–756.  Errata
  138. R. Schumer; D. A. Benson; M.M. Meerschaert and B. Baeumer, Fractal mobile/immobile solute transport, Water Resources Research, Vol. 39 (2003), No. 10, p. 1296 (12 pp.), doi:10.1029/2003WR002141.
  139. T.J. Kozubowski, M.M. Meerschaert and H.P. Scheffler, The operator nu-stable laws, Publ. Math. Debrecen, Vol. 63 (2003), No. 4, pp. 569-585.
  140. P. Becker-Kern, M.M. Meerschaert and H.P. Scheffler, Hausdorff dimension of operator stable sample paths, Monatshefte fur Mathematik, Vol. 140 (2003), No. 2, pp. 90-101.
  141. M.M. Meerschaert and H.P. Scheffler, Nonparametric methods for heavy tailed vector data:  A survey with applications from finance and hydrology, Recent advances and trends in nonparametric statistics, pp. 265-279, M. G.  Akritas and D.N. Politis, Eds., Elsevier Science (2003), ISBN 0-444-51378-7.
  142. M.M. Meerschaert and H.P. Scheffler, Portfolio modeling with heavy tailed random vectors, Handbook of Heavy-Tailed Distributions in Finance, pp. 595-640, S. T. Rachev, Ed., Elsevier North-Holland, New York (2003) ISBN 0-444-50896-1.
  143. R. Schumer, D. A. Benson, M.M. Meerschaert and B. Baeumer, Multiscaling fractional advection-dispersion equations and their solutions, Water Resources Research, Vol. 39 (2003) No. 1, pp. 1022-1032, article 10.1029/2001WR000756.
  144. M.M. Meerschaert and S. Sepanski, Regular variation and the functional central limit theorem for heavy tailed random vectors. Institut Mathématique. Publications. Nouvelle Série  (Belgrade Mathematics Institute Publications, New Series), Vol. 71 (2002), pp. 55-62.
  145. M.G. Herrick, D.A. Benson, M.M. Meerschaert and K.R. McCall, Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system, Water Resources Research, Vol. 38 (2002), No. 11, pp. 1227-1239, article 10.1029/2001WR000914.
  146. M.M. Meerschaert, D.A. Benson, H.P. Scheffler, and P. Becker-Kern, Governing equations and solutions of anomalous random walk limits, Physical Review E, Vol. 66 (2002) No. 6, pp. 102R-105R.
  147. M.M. Meerschaert, D.A. Benson, H.P. Scheffler, and B. Baeumer, Stochastic solution of space-time fractional diffusion equations. Physical Review E, Vol. 65 (2002), No. 4, pp. 1103-1106.
  148. M.M. Meerschaert and H.P. Scheffler, Semistable Lévy motionFractional Calculus and Applied Analysis,Vol. 5 (2002), No. 1, pp. 27-54.
  149. M.M. Meerschaert and H.P. Scheffler, Limit Distributions for Sums of Independent Random Vectors:  Heavy Tails in Theory and Practice. Wiley & Sons, New York, 2001, xiv+486 pp., ISBN 0-471-35629-8. 
  150. B. Baeumer and M.M. Meerschaert, Stochastic solutions for fractional Cauchy problemsFractional Calculus and Applied Analysis, Vol. 4 (2001), No. 4, pp. 481-500.
  151.  I.B. Aban and M.M. Meerschaert, Shifted Hill's estimator for heavy tails. Communications in Statistics: Simulation and Computation, Vol. 30 (2001), No. 4, pp. 949-962.
  152. M.M. Meerschaert and H.P. Scheffler, Sample cross-correlations for moving averages with regularly varying tails. Journal of Time Series Analysis,  Vol. 22 (2001), No. 4, pp. 481-492.
  153. B. Baeumer, D. A. Benson, M.M. Meerschaert and S. W. Wheatcraft, Subordinated advection-dispersion equation for contaminant transport. Water Resources Research, Vol. 37 (2001), No. 6, pp. 1543-1550.
  154. R. Schumer, D. A. Benson, M.M. Meerschaert and S. W. Wheatcraft, Eulerian derivation of the fractional advection-dispersion equation. Journal of Contaminant Hydrology, Vol. 38 (2001), pp. 69-88.
  155. D.A. Benson, R. Schumer, M.M. Meerschaert and S. W. Wheatcraft, Fractional dispersion, Lévy motion, and the MADE tracer testsTransport in Porous Media, Vol. 42 (2001), pp. 211-240.
  156.  M.M. Meerschaert, D.A. Benson, and B. Baeumer, Operator Lévy motion and multiscaling anomalous diffusion. Physical Review E, Vol. 63 (2001), pp. 021112-021117.
  157. M.M. Meerschaert and H.P. Scheffler, Moving averages of random vectors with regularly varying tails, Journal of Time Series Analysis, Vol. 21 (2000), pp. 297-328.
  158. M.M. Meerschaert and H.P. Scheffler, Limit laws for symmetric k-tensors of regularly varying measures, Journal of Multivariate Analysis, vol. 73 (2000), pp. 241-261.
  159. D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, The fractional-order governing equation of Lévy motion, Water Resources Research, Vol. 36 , No. 6 (2000), pp. 1413-1424.
  160. D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resources Research, Vol. 36 , No. 6 (2000), pp. 1403-1412.
  161. M.M. Meerschaert and H.P. Scheffler, One dimensional marginals of operator stable laws and their domains of attraction, Publicationes Mathematicae Debrecen, Vol. 55 (1999), No. 3-4, pp. 487-499.
  162. M.M. Meerschaert and H.P. Scheffler, Spectral decomposition for operator-self-similar processes and their generalized domains of attraction, Stochastic Processes and Their Applications , Vol. 84 (1999) pp. 71-80.
  163. M.M. Meerschaert and H.P. Scheffler, Moment estimator for random vectors with heavy tails, Journal of Multivariate Analysis, vol. 71 (1999), No. 1, pp. 145-159.
  164. P.L. Anderson, M.M. Meerschaert and A.V. Vecchia, Innovations algorithm for periodically stationary time series.  Stochastic Processes and Their Applications, Vol. 83 (1999) pp. 149-169.
  165. M.M. Meerschaert and H.P. Scheffler, Sample covariance matrix for random vectors with heavy tails, Journal of Theoretical Probability, Vol. 12 (1999), No. 3, pp. 821-838.
  166. W. B. Whiting, V. R. Vasquez, M.M. Meerschaert, Techniques for assessing the effects of uncertainties in thermodynamic models and data, Fluid Phase Equilibria, Vol. 158-160 (1999) pp. 627-641. 
  167. M.M. Meerschaert, D.A. Benson, and B. Baeumer, Multivariable advection and fractional dispersion, Physical Review E, Vol. 59 (1999) No. 5, pp. 5026-5028.
  168. M.M. Meerschaert and H.P. Scheffler, Multivariable regular variation of functions and measures, Journal of Applied Analysis, Vol. 5 (1999), No. 1, pp. 125-146.
  169. M.M. Meerschaert, Mathematical Modeling , 2nd Edition, Academic Press, 1999.
  170. M.M. Meerschaert and H.P. Scheffler, A simple robust estimation method for the thickness of heavy tails, Journal of Statistical Planning and Inference, Vol. 71 (1998), No. 1-2, pp. 19-34. 
  171. P.L. Anderson and M.M. Meerschaert, Modeling river flows with heavy tails, Water Resources Research, Vol. 34 (1998)  No. 9, pp. 2271-2280.
  172. M.M. Meerschaert and H.P. Scheffler, Convergence of semitypes, Publicationes Mathematicae Debrecen , Vol. 53 (1998), No. 1-2, pp. 119-131.
  173. P.L. Anderson and M.M. Meerschaert, Periodic moving averages of random variables with regularly varying tails, The Annals of Statistics, Vol. 25 (1997), No. 2, pp. 771-185.
  174. M.M. Meerschaert and H.P. Scheffler, The structure of generalized domains of semistable attraction, Statistics and Probability Letters, Vol. 33 (1997), pp. 367-372.
  175. M.M. Meerschaert and H.P. Scheffler, Spectral decomposition for generalized domains semistable of attraction, The Journal of Theoretical Probability, Vol. 10 (1997), No. 1, pp. 51-71.
  176. M.M. Meerschaert and H.P. Scheffler, Series representation for semistable laws and their domains of semistable attraction, The Journal of Theoretical Probability, Vol. 9 (1996) No. 4, pp. 931-959.
  177. M.M. Meerschaert and H.P. Scheffler, Generalized domains of semistable attraction of nonnormal laws, The Journal of Applied Analysis, Vol. 2 (1996), No. 2, pp. 203-215.
  178. C. Gupta and M.M. Meerschaert, Mathematical modeling experience for teachers, Proceedings of the Second Biannual Symposium of Mathematical Modeling, June 13-15, 1996.
  179.  M.M. Meerschaert and J.A. Veeh, Symmetry Groups in d-Space, Statistics and Probability Letters , Vol. 22 (1995), No. 1, pp. 1-6.
  180. M.M. Meerschaert, Norming Operators for Generalized Domains of Attraction, Journal of Theoretical Probability, Vol. 7 (1994), pp. 793-798.
  181. V. Mandrekar, M.M. Meerschaert, Sample Moments and Symmetric Statistics, Stochastic Analysis on Infinite Dimensional Spaces, Pitman Research Notes in Mathematics, Vol. 310 (1994), pp. 197-210.
  182. M.M. Meerschaert, Mathematical Modeling , Academic Press, 1993.
  183.  M.M. Meerschaert, Regular Variation and Generalized Domains of Attraction in Rk , Statistics and Probability Letters, Vol. 18 (1993) No. 2, pp. 233-239.
  184. M.M. Meerschaert and J.A. Veeh, The Structure of the Exponents and Symmetries of an Operator Stable Law, Journal of Theoretical Probability, Vol. 6 (1993), No. 4, 713-726.
  185. M.M. Meerschaert, Pseudomoments for Generalized Domains of Attraction, Proceedings of the American Mathematical Society, vol. 113 (1991), pp. 1071-1075.
  186. M.M. Meerschaert, Regular Variation in Rk and Vector-Normed Domains of Attraction, Statistics and Probability Letters, vol. 11 (1991), pp. 287-289.
  187. M.M. Meerschaert, Spectral Decomposition for Generalized Domains of Attraction, The Annals of Probability, vol. 19 (1991), pp. 875-892.
  188. M.M. Meerschaert, Computing the Symmetries and Exponents of Operator-Stable Laws, Proceedings of the 22nd Symposium on the Interface between Computer Science and Statistics, May 1990, 461-462.
  189. M.M. Meerschaert, Moments of Random Vectors which Belong to Some Domain of Normal Attraction, The Annals of Probability, vol. 18 (1990), pp. 870-876.
  190. M.M. Meerschaert, W. Rainaldi, R. Smith, D. Thompson, C. Frederick, and K. Wheaton, Embedded Training Software Specifications for the FOG-M System Demonstration, Research Product 89-05, Manned Systems Group, Systems Research Laboratory, U.S. Army Research Institute for the Behavioral and Social Sciences, 1989.
  191. M.M. Meerschaert, AMS Referendum, letter to the editor, Notices of the American Mathematical Society, vol. 36 (1989).
  192. M.M. Meerschaert, W. P. Cherry, Modelling the Performance of a Scanning Radio Communications Sensor, Naval Research Logistics Quarterly, vol. 35 (1988), pp. 307-315.
  193. M.M. Meerschaert, Regular Variation in Rk, Procedings of the American Mathematical Society, vol. 102 (1988), pp. 341-348.
  194. M.M. Meerschaert, Domains of Attraction of Nonnormal Operator-Stable Laws, Journal of Multivariate Analysis, vol. 19 (1986), pp. 342-347.
  195.  M.M. Meerschaert, Regular Variation and Domains of Attraction in Rk, Statistics and Probability Letters, vol. 4 (1986), pp. 43-45.
  196. M.M. Meerschaert, Multivariable Domains of Attraction and Regular Variation, Doctoral Thesis, The University of Michigan, August 1984.
  197. Gary Witus, Robert W. Blum, and M.M. Meerschaert, Analysis of Information Flow in the Tactical Operations System, Research Note 80-12, Human Factors Technical Area, U.S. Army Research Institute for the Behavioral and Social Sciences, May1980.
  198. Gary Witus, M.M. Meerschaert, and  Donald Kleist, Programmer's Manual for the Tactical Operations System Analysis Package, Research Note 80-15, Human Factors Technical Area, U.S. Army Research Institute for the Behavioral and Social Sciences, May1980.