PUBLICATIONS
- 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. 161–178.
Special Issue on Modern fractional
dynamic systems and
applications.
- 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.
- 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. 598–617.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M.M. Meerschaert, H.-P.
Scheffler, and S. Stoev, Extreme value
theory with operator norming,
Extremes, Vol. 16 (2013),
No. 4, pp. 407–428.
- 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.
- 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
- 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.
- 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.
- M.M. Meerschaert and Farzad Sabzikar, Tempered
Fractional Brownian Motion, Statistics
and Probability Letters, Vol. 83 (2013), No. 10, pp. 2269–2275.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M.M. Meerschaert, Mathematical
Modeling, 4th Edition (2013), Academic Press, ISBN
978-0-12-386912-8.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M.M. Meerschaert, Fractional
Calculus, Anomalous Diffusion, and Probability, Fractional Dynamics, R. Metzler and
J. Klafter, Eds., World Scientific, Singapore, pp. 265--284, 2012.
- A.
Jurlewicz, M.M. Meerschaert, and H.P. Scheffler, Cluster continuous time random
walks, Studia Mathematica,
Vol. 205 (2011), No. 1, pp.13--30.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- A. Kumar, M.M. Meerschaert, and P.
Vellaisamy, Fractional Normal Inverse Gaussian Diffusion,
Statistics and Probability Letters, Vol. 81 (2011) pp. 146–152.
- 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.
- B. Baeumer, M. M. Meerschaert and M. Naber, Stochastic
models for relativistic diffusion, Physical Review E, Vol. 82
(2010), pp. 011132.
- 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.
- 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.
- 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.
- 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.
- 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.
- B. Baeumer, M.M. Meerschaert and
E. Nane, Space-time
duality
for fractional diffusion, Journal
of Applied Probability, Vol. 46 (2009), pp. 1100-1115.
- 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.
- P. Chakraborty, M. M. Meerschaert, and
C. Y. Lim, Parameter Estimation for Fractional
Transport: A particle tracking approach, Water Resources Research, Vol. 45
(2009), W10415, doi:10.1029/2008WR007577.
- 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.
- 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.
- 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.
- M.M. Meerschaert, E. Nane, Y. Xiao, Correlated
continuous time random walks, Statistics
and Probability Letters, Vol. 79 (2009), pp. 1194-1202.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- M.M. Meerschaert, S.W. Wheatcraft, Fractional
Conservation of Mass, Advances in Water Resources, Vol.
31 (2008), pp. 1377–1381.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- D.A. Benson, R. Schumer, M.M. Meerschaert, Extreme
events with power law interarrivals, Geophysical Research Letters, Vol. 34 (2007), No. 16, L16404.
- 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.
- M.M. Meerschaert, Mathematical
Modeling , 3rd Edition, Academic Press, 2007, ISBN
978-0-12-370857-1.
- 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.
- H. Biermé, M.M. Meerschaert,
H.P. Scheffler, Operator
Scaling Stable Random Fields, Stochastic Processes and their
Applications, Vol. 117 (2007), pp. 312–332.
- 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.
- B. Baeumer, M.M. Meerschaert, Fractional diffusion with two time scales, Physica A:
Statistical Mechanics and Its Applications, Vol. 373 (2007), pp.
237–251
- 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.
- T.J. Kozubowski, M.M. Meerschaert, K.
Podgórski, Fractional Laplace Motion,
Advances in Applied Probability, Vol. 38 (2006), No. 2, pp.
451-464.
- 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).
- 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.
- 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 information. Conference Proceedings for MODFLOW and
MORE 2006: Managing Ground-Water Systems, International Ground
Water Modeling Center, pp. 639-643.
- M.M. Meerschaert, H.P. Scheffler, Stochastic model for ultraslow diffusion, Stochastic Processes and Their Applications,
Vol. 116 (2006), No. 9, pp. 1215-1235.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M.M. Meerschaert and H.P. Scheffler, Semistable
Lévy motion. Fractional Calculus and Applied
Analysis,Vol.
5 (2002), No. 1, pp. 27-54.
- 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.
- B. Baeumer and M.M. Meerschaert, Stochastic
solutions
for fractional Cauchy problems. Fractional
Calculus and Applied Analysis, Vol. 4 (2001), No. 4, pp. 481-500.
- 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.
- 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.
- 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.
- 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.
- D.A. Benson, R. Schumer, M.M. Meerschaert and S. W. Wheatcraft, Fractional dispersion, Lévy motion, and the MADE
tracer tests. Transport in Porous Media, Vol. 42
(2001), pp. 211-240.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M.M. Meerschaert, Mathematical
Modeling , 2nd Edition, Academic Press, 1999.
- 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.
- P.L. Anderson and M.M. Meerschaert, Modeling
river flows with heavy tails, Water Resources Research,
Vol. 34 (1998) No. 9, pp. 2271-2280.
- M.M. Meerschaert and H.P. Scheffler, Convergence
of semitypes, Publicationes Mathematicae Debrecen , Vol. 53
(1998), No. 1-2, pp. 119-131.
- 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.
- 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.
- 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.
- 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.
- 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.
- C. Gupta and M.M. Meerschaert, Mathematical modeling experience
for teachers, Proceedings of the Second Biannual Symposium of
Mathematical Modeling, June 13-15, 1996.
- M.M. Meerschaert and J.A. Veeh, Symmetry
Groups in d-Space, Statistics and Probability Letters ,
Vol. 22 (1995), No. 1, pp. 1-6.
- M.M. Meerschaert, Norming Operators for Generalized Domains of
Attraction, Journal of Theoretical Probability, Vol. 7 (1994),
pp. 793-798.
- 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.
- M.M. Meerschaert, Mathematical
Modeling , Academic Press, 1993.
- M.M. Meerschaert, Regular Variation
and Generalized Domains of Attraction in Rk , Statistics
and Probability Letters, Vol. 18 (1993) No. 2, pp. 233-239.
- 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.
- M.M. Meerschaert, Pseudomoments for
Generalized Domains of
Attraction, Proceedings of the American Mathematical Society,
vol. 113 (1991), pp. 1071-1075.
- M.M. Meerschaert, Regular Variation in Rk
and Vector-Normed Domains of Attraction, Statistics
and Probability Letters, vol. 11 (1991), pp. 287-289.
- M.M. Meerschaert, Spectral Decomposition for Generalized Domains
of Attraction, The Annals of Probability, vol. 19 (1991), pp.
875-892.
- 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.
- 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.
- 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.
- M.M. Meerschaert, AMS Referendum, letter to the editor, Notices
of the American Mathematical Society, vol. 36 (1989).
- 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.
- M.M. Meerschaert, Regular Variation in Rk,
Procedings of the American Mathematical Society, vol. 102
(1988), pp. 341-348.
- M.M. Meerschaert, Domains of Attraction
of Nonnormal Operator-Stable Laws, Journal of Multivariate
Analysis, vol. 19 (1986), pp. 342-347.
- M.M. Meerschaert, Regular Variation
and Domains of Attraction in Rk, Statistics and
Probability Letters, vol. 4 (1986), pp. 43-45.
- M.M. Meerschaert, Multivariable Domains of Attraction and
Regular Variation, Doctoral Thesis, The University of Michigan,
August 1984.
- 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.
- 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.