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, 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.

• Space-time duality for fractional diffusion, 6th International Conference on Levy Processes, Dresden, July 2010 (with Boris Baeumer, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand; Paramita Chakraborty, Department of Mathematics, California State University, Bakersfield; James Kelly, USA Naval Postgraduate School; Peter Kern, Department of Mathematics, Heinrich-Heine-University, Düsseldorf, Germany; Chae Young Lim, Department of Statistics and Probability, Michigan State; Robert McGough, Department of  Electrical and Computer Engineering, Michigan State; Erkan Nane, Department of Mathematics and Statistics, Auburn University; Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany; Yimin Xiao, Department of Statistics and Probability, Michigan State University; and Yong Zhang, Desert Research Institute, Las Vegas Nevada).
• 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).
  
• Continuous time random walks, fractional calculus, and applications,  Department of Mathematics Colloquium, Tufts University, October 2009 (with I. B. Aban, Department of Biostatistics, University of Alabama at Birmingham; Paul Anderson, Department of Mathematics and Computer Science, Albion College, Boris Baeumer; Peter Becker-Kern; David A. Benson, Geology and Geological Engineering, Colorado School of Mines; Paramita Chakraborty; James Kelly; Mihály Kovács, Mathematics & Statistics, University of Otago, Dunedin, New Zealand; Chae Young Lim; Robert McGough; Erkan Nane; Anna K. Panorska, Department of Mathematics and Statistics, University of Nevada, Reno; Parthanil Roy, Department of Statistics and Probability, Michigan State University; Enrico Scalas, Università del Piemonte Orientale, Alessandria, Italy; Hans-Peter Scheffler; Rina Schumer, Water Resources, Desert Research Institute, Reno Nevada; Qin Shao, Department of Mathematics, University of Toledo, Ohio; P. Vellaisamy; Stephen W. Wheatcraft, Geological Sciences, University of Nevada, Reno; Yimin Xiao; and Yong Zhang).
• Space-time duality for fractional diffusion, Department of Statistics and Probability Colloquium, Michigan State University, September 2009 (with Boris Baeumer; Peter Becker-Kern; Paramita Chakraborty; James Kelly; Mihaly Kovacs; V. Mandrekar, Department of Statistics and Probability, Michigan State University; Robert McGough; Erkan Nane; Parthanil Roy;  Enrico Scalas;  Hans-Peter Scheffler; Rina Schumer; Qin Shao; and Yimin Xiao).
  
• Tempered stable models for anomalous diffusion,  Department of Mathematics Colloquium, University of Tennessee, September 2009 (with I. B. Aban; Boris Baeumer; Peter Becker-Kern; David A. Benson; James Kelly; Mihály Kovács; Robert McGough; Erkan Nane; Anna K. Panorska; Parthanil Roy; Hans-Peter Scheffler; Rina Schumer; Qin Shao; P. Vellaisamy; and Yong Zhang).
• The Fractal Calculus Project,  Department of Mathematics Junior Colloquium, University of Tennessee, September 2009 (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; Stephen W. Wheatcraft; and Yimin Xiao).

• Stochastic models for relativistic diffusion,  Physical Review E, to appear (with Boris Baeumer, Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand; and Mark Naber, Department of Mathematics, Monroe County Community College, Monroe, MI).
• Asymptotic results for Fourier-PARMA time series, Journal of Time Series Analysis, to appear (with Yonas Gebeyehu Tesfaye, Hydrologist, GEI Consultants, Inc., Rancho Cordova, California; and Paul L. Anderson, Department of Mathematics, Albion College, Michigan).
• Parameter estimation for tempered power law distributions, (with Parthanil Roy, Department of Statistics and Probability, Michigan State University; and Qin Shao, Department of Mathematics, University of Toledo).  Click here to download R code and data sets used in this paper. 
  
• A-Collapsibility of Distribution Dependence and Quantile Regression Coefficients (with P. Vellaisamy, Department of Mathematics, Indian Institute of Technology Bombay, India).
• Distributed-order fractional Cauchy problems on bounded domains (with Erkan Nane, Department of Mathematics and Statistics, Auburn University; and P. Vellaisamy).
• Modeling and simulation with operator scaling (with Serge Cohen, Université Paul Sabatier, Laboratoire de Statistique et de Probabilités, Toulouse, France; and Jan Rosiński, Department of Mathematics, University of Tennessee, Knoxville).  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.
  
• Fernique-type inequalities and exact moduli of continuity for anisotropic Gaussian random fields (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).
  
• Extremal behavior of a coupled continuous time random walk (with Rina Schumer, Division of Hydrologic Sciences, Desert Research Institute, Reno, NV 89512; and Boris Baeumer).
• Tempered fractional Cauchy problems on bounded domains (with Erkan Nane and P. Vellaisamy).
• Anticipating Continuous Time Random Walks (with Agnieszka Jurlewicz, Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland; Peter Kern, Mathematical Institute, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany; and Hans-Peter Scheffler, Fachbereich Mathematik, Universität Siegen, 57068 Siegen, Germany).
  
• Tempered stable laws as random walk limits (with Arijit Chakrabarty, Department of Mathematics, Indian Institute of Science, Bengaluru 560012, India).
• The Fractional Normal Inverse Gaussian Process as the Limit of a Continuous Time Random Walk (with A. Kumar and P. Vellaisamy, Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India).
• The fractional Poisson process and the inverse stable subordinator (with Erkan Nane, Department of Mathematics and Statistics, Auburn University; and P. Vellaisamy, Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India).