Mark M. Meerschaert

Mark M. Meerschaert is Chairperson of the Department of Statistics and Probability  at Michigan State University and an Adjunct Professor in the Department of Physics at the University of Nevada .  Professor 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, 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 textbook Mathematical Modeling , 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.

• The fractal calculus project:  Broad spectrum mathematics, Mathematics Colloquium, Central Michigan University, April 2008  (with Paul Anderson, Department of  Statistics and Probability, Michigan State University; Boris Baeumer, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand; Peter Becker-Kern, Department of Mathematics, University of Dortmund, Germany; David A. Benson, Department of Geology and Geological Engineering, Colorado School of Mines; James Kelly, Department of  Electrical and Computer Engineering, Michigan State University; Mihály Kovács, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand; Robert McGough, Department of  Electrical and Computer Engineering, Michigan State University; Erkan Nane, Department of  Statistics and Probability, Michigan State University; Enrico Scalas, Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Alessandria, Italy; Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany; Rina Schumer, Desert Research Institute, Reno, Nevada; and Yimin Xiao, Department of  Statistics and Probability, Michigan State University). 
• The fractal calculus project, College of Science and Engineering Colloquium, Saginaw Valley State University, Michigan, April 2008  (with Paul Anderson; Boris Baeumer; Peter Becker-Kern,; David A. Benson,; James Kelly; Mihály Kovács; Robert McGough; Erkan Nane; Enrico Scalas; Hans-Peter Scheffler; Rina Schumer; and Yimin Xiao).  
• Fractional Calculus, heavy tails, and applications, Mathematics Colloquium, University of Toledo, November 2007.
• Tail parameter estimation, Stochastic Transport and Emergent Scaling in Earth-surface Processes.   Tahoe Center for Environmental Research, Incline Village, Nevada, November 2007.
• Scaling limits and governing equations, Stochastic Transport and Emergent Scaling in Earth-surface Processes.   Tahoe Center for Environmental Research, Incline Village, Nevada, November 2007.
• Stochastic model for mobile-immobile flow and transport, Annual Meeting of the Geological Society of America, Denver, October 2007. (with Boris Baeumer; Peter Becker-Kern; David A. Benson; Hans-Peter Scheffler; Rina Schumer, Desert Research Institute, Reno, Nevada; and Yong Zhang, Desert Research Institute, Las Vegas, Nevada).
• Fractional Diffusion, Department of Aerospace and Mechanical Engineering, Notre Dame University, South Bend, Indiana, October 2007.
• Triangular array limits for continuous time random walks, 5th International Conference on Lévy Processes, Copenhagen, Denmark, August 2007 (with Hans-Peter Scheffler). 
• Fractional diffusion: A new paradigm, 2007 Inverse Problems Symposium, Michigan State University, June 2007 (with Boris Baeumer; Peter Becker-Kern; David A. Benson; Mihály Kovács, Department of Mathematics & Statistics, University  of Otago, Dunedin, New Zealand; Hans-Peter Scheffler; Rina Schumer; Stephen W. Wheatcraft, Department of Geological Sciences, University of Nevada, Reno; and Yimin Xiao, Department of Statistics and Probability, Michigan State University).
• Fractional Calculus and Brownian time, Probability Seminar, University of Illinois at Urbana-Champaign, March 2007 (with Inmaculada B. Aban, Department of Biostatistics, School of Public Health, University of Alabama at Birmingham; Paul L. Anderson, Department of Mathematics, Albion College; Boris Baeumer; David A. Benson; Erkan Nane, Department of Statistics and Probability, Michigan State University; Anna K. Panorska, Department of Mathematics and Statistics, University of Nevada, Reno; Hans-Peter Scheffler; Rina Schumer; Stephen W. Wheatcraft; and Yimin Xiao).

•  Subordinated multiparameter groups of linear operators: Properties via the transference principle, To appear in Functional Analysis and Evolution Equations, Dedicated to Gunter Lumer. Editors: H. Amann, W. Arendt, M. Hieber, R. Nagel, F. Neubrander, S. Nicaise. Birkhaeuser Verlag (with Boris Baeumer and Mihaly Kovacs, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand).
• Brownian subordinators and fractional Cauchy problems, Transactions of the American Mathematical Society, to appear (with Boris Baeumer; and Erkan Nane, Department of Mathematics and Statistics, Auburn University).
  
• Fractional Conservation of Mass, Advances in Water Resources, to appear (with Stephen W. Wheatcraft, Department of Geologic Sciences, University of Nevada, Reno).
• Tempered anomalous diffusion in heterogeneous systems, Geophysical Research Letters, to appear (with Yong Zhang and Boris Baeumer).
• Time-Domain 3D Green’s Functions for Power Law Media, Journal of the Acoustical Society of America, to appear (with James F. Kelly and Robert J. McGough, Department of Electrical and Computer Engineering, Michigan State University).
• Fractional Cauchy problems on bounded domains, The Annals of Probability, to appear (with Erkan Nane; and P. Vellaisamy,  Department of Mathematics,  Indian Institute of Technology, Bombay).
• Extremal limit theorems for observations separated by random waiting times (with Stilian Stoev, Department of Statistics, University of Michigan).
• Local Whittle estimator for anisotropic random fields  (with Hongwen Guo, Educational Testing Service, Princeton, New Jersey; and Chae Young Lim, Department of Statistics and Probability, Michigan State University).
• A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations (with David A. Benson).
  
• Tempered stable Levy motion and transient super-diffusion (with Boris Baeumer).
• Particle tracking for time-fractional diffusion (with Yong Zhang and Boris Baeumer).