Mark M. Meerschaert

Mark M. Meerschaert is a Professor in the Department of Statistics and Probability at Michigan State University.  Meerschaert has professional experience in the areas of probability, statistics, statistical physics, mathematical modeling, operations research, partial differential equations, ground water and surface water hydrology. He started his professional career in 1979 as a systems analyst at Vector Research, Inc. of Ann Arbor and Washington D.C., where he worked on a wide variety of modeling projects for government and industry. Meerschaert earned his doctorate in Mathematics from the University of Michigan in 1984. He has taught at the University of Michigan, Albion College, Michigan State University, the University of Nevada in Reno, and the University of Otago in Dunedin, New Zealand. His current research interests include limit theorems and parameter estimation for infinite variance probability models, heavy tail models in finance, modeling river flows with heavy tails and periodic covariance structure, medical imaging, anomalous diffusion, continuous time random walks, fractional derivatives and fractional partial differential equations, and ground water flow and transport.

See below for some recent preprints.  Click here a complete list of publications, information about the Academic Press textbook Mathematical Modeling (the 4th edition will be released in late 2012), the new De Gruyter textbook Stochastic Models for Fractional Calculus, or the research monograph Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice.


RECENT PAPERS AND TALKS in PDF format:  Click below to download.  Click here for a free PDF viewer.

• Stable Laws, Fractional Calculus, and Medical Ultrasound, International Conference on Long-Range Dependence, Self-Similarity and Heavy Tails, in Honor of Professor Murad S. Taqqu, Research Triangle Park, North Carolina, USA, April  2012 (with Peter Straka, Department of Statistics and Probability, Michigan State University; Yuzhen Zhou, Department of Statistics and Probability, Michigan State University; Robert McGough, Electrical and Computer Engineering, Michigan State University; Boris Baeumer, Mathematics & Statistics, University of Otago, Dunedin, New Zealand; David Benson, Geology and Geological Engineering, Colorado School of Mines; James Kelly, Naval Postgraduate School, Monterey, California; Erkan Nane, Department of Mathematics and Statistics, Auburn University; Peter Kern, Department of Mathematics, Heinrich Heine University, Duesseldorf, Germany; Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany; Rina Schumer, Water Resources, Desert Research Institute, Reno NV; Alla Sikorskii, Department of Statistics and Probability, Michigan State University; and Yimin Xiao, Department of Statistics and Probability).
• Modeling and simulation with tempered stable laws, 5th International Conference on Computational and Financial Econometrics, London, England, December 2011 (with Inmaculada B. Aban, Department of Biostatistics, School of Public Health, University of Alabama at Birmingham; Boris Baeumer; Anna K. Panorska, Department of Mathematics and Statistics, University of Nevada, Reno; Parthanil Roy, India Statistical Institute, Calcutta; Hans-Peter Scheffler; Qin Shao, Department of Mathematics, University of Toledo; and Yong Zhang, Desert Research Institute, Las Vegas, Nevada, USA).
• Statistical Modeling of Hydraulic Conductivity Fields, Annual Meeting of the American Geophysical Union, San Francisco, December 2011 (with Boris Baeumer; David A. Benson; Geoffrey Bohling, Kansas Geological Survey, Lawrence, Kansas; Mine Dogan, Department of Geological Sciences, Michigan State University; David Hyndman, Department of Geological Sciences, Michigan State University; Tomasz J. Kozubowski, Dept. of Mathematics and Statistics, Univ. of Nevada, Reno; Silong Lu, Tetra Tech, Inc., Atlanta, GA; Fred J. Molz, Dept. of Environmental Engineering & Science, Clemson University; and Hans-Peter Scheffler).
• Fractional Diffusion, Radiology Seminar, University of Illinois at Chicago,  November 2011 (with Boris Baeumer; Warren Barrash, Department of Geosciences, Boise State University; David A. Benson; Paramita Chakraborty, Mathematics, California State University, Bakersfield; Bill X. Hu, Department of Geological Sciences, Florida State University; Changming He, Delaware Geological Survey, University of Delaware, Newark; Luanjing Guo, Department of Geological Sciences, Florida State University; David Hyndman; James F. Kelly; Peter Kern; Mihály Kovács, Mathematics & Statistics, University of Otago, Dunedin, New Zealand; Eric M. LaBolle, Land, Air, and Water Resources, University of California, Davis; Xinya Li, Department of Geological Sciences, Florida State University; Chae Young Lim, Department of Statistics and Probability, Michigan State University; Robert J. McGough;  Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii, Statistics and Probability, Michigan State University; Charles Tadjeran, Sierra Nevada Corporation; Stephen W. Wheatcraft, Geological Sciences, University of Nevada, Reno; Yimin Xiao, Statistics and Probability, Michigan State University; Yong Zhang, Desert Research Institute, Las Vegas NV.).
• Fractional Diffusion, Environmental Fluid Dynamics (EFD) Seminar, University of Notre Dame, November 2011 (with Boris Baeumer; Warren Barrash; David A. Benson; Paramita Chakraborty; Bill X. Hu; Changming He; Luanjing Guo; David Hyndman; James F. Kelly; Peter Kern; Mihály Kovács; Eric M. LaBolle; Xinya Li,; Robert J. McGough; Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii; Charles Tadjeran; Stephen W. Wheatcraft; Yimin Xiao; Yong Zhang).
• Space-time duality for fractional diffusion, 6th International Conference on Lévy Processes, Dresden, July 2010 (with Boris Baeumer; Paramita Chakraborty; James Kelly; Peter Kern; Chae Young Lim; Robert McGough; Erkan Nane; Hans-Peter Scheffler; Yimin Xiao, Department of Statistics and Probability, Michigan State University; and Yong Zhang).
• Fractional Cauchy problems on bounded domains, International Indian Statistical Association Conference,  January 2010, Visakhapatnam, India (with Boris Baeumer; Peter Kern; Erkan Nane; Hans-Peter Scheffler; Yimin Xiao; and P. Vellaisamy, Department of Mathematics, India Institute of Technology, Bombay, India).
  

• Transient anomalous sub-diffusion on bounded domains, Proceedings of the American Mathematical Society, to appear (with Erkan Nane; and P. Vellaisamy).
• Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields, Transactions of the American Mathematical Society, to appear (with Wensheng Wang, School of Finance and Statistics, East China Normal University, and Department of Mathematics, Hangzhou Normal University; and Yimin Xiao, Department of Statistics and Probability, Michigan State University).
• Fractional governing equations for coupled random walks, Computers and Mathematics with Applications, to appear in the Special Issue on Advances in Fractional Differential Equations III (with Agnieszka Jurlewicz; Peter Kern, Mathematical Institute, Heinrich-Heine-Universität Düsseldorf, Germany; and Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany).  Click here to download R codes used in this paper.
• Tauberian theorems for matrix regular variation, Transactions of the American Mathematical Society, to appear (with Hans-Peter Scheffler).
• Clustered continuous time random walks: Diffusion and relaxation consequences, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, to appear (with Karina Weron, Institute of Physics, Wrocław University of  Technology, Poland; Aleksander Stanislavsky, Institute of Radio Astronomy, Kharkov, Ukraine; Agnieszka Jurlewicz, Institute of Mathematics and Computer Science, Wrocław University of  Technology, Poland; and Hans-Peter Scheffler).
• Fractional calculus in hydrologic modeling: A numerical perspective, Advances in Water Resources, to appear (with David A. Benson and Jordan Revielle, Hydrological Science and Engineering, Colorado School of Mines).
• Fractal dimensions for continuous time random walk limits (with Erkan Nane; and Yimin Xiao).
• Fractional Pearson diffusion (with Nikolai N. Leonenko, Cardiff School of Mathematics, Cardiff University; and Alla Sikorskii, Department of Statistics and Probability, Michigan State University).
• A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media (with HongGuang Sun, College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China; Yong Zhang, Division of Hydrologic Sciences, Desert Research Institute, Las Vegas; Jianting Zhu, Division of Hydrologic Sciences, Desert Research Institute, Las Vegas; and Wen Chen, College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China).
  
• Inverse stable subordinators (with Peter Straka, Department of Statistics and Probability, Michigan State University).
• Stochastic solution to a time-fractional attenuated wave equation (with Peter Straka; Yuzhen Zhou, Department of Statistics and Probability, Michigan State University; and Robert J. McGough, Electrical and Computer Engineering, Michigan State University).
• Product rule for vector fractional derivatives (with Alla Sikorskii; and Diogo Bolster, Department of Civil Engineering and Geological Sciences, University of Notre Dame).
• Numerical methods for solving the multi-term time-fractional wave-diffusion equations (with F. Liu, Mathematical Sciences, Queensland University of Technology, Brisbane, Australia; R.J. McGough;
  P. Zhuang and Q. Liu, School of Mathematical Sciences, Xiamen University, Xiamen, China).