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 for his resume, a complete list of publications, information about the Academic Press textbook Mathematical Modeling, the 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.

• Fractional Calculus Models for Anomalous Diffusion, Department of Mathematics, Tulane University, December 2012 (with David Benson, Department of Geological Engineering, Colorado School of Mines;  Hermine Biermé, Université René Descartes, Paris, France; Serge Cohen, Université Paul Sabatier, Laboratoire de Statistique et de Probabilités, Toulouse, France; Mine Dogan, Department of Geological Sciences, Michigan State University; David Hyndman, Department of Geological Sciences, Michigan State University; Jan Rosiński, Department of Mathematics, University of Tennessee, Knoxville; Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany; Rina Schumer, Department of Hydrological Sciences, Desert Research Institute, Reno, Nevada; Alla Sikorskii, Department of Statistics and Probability, Michigan State University; Remke L. Van Dam, Department of Geological Sciences, Michigan State University; and Stephen W. Wheatcraft, Geological Sciences, University of Nevada, Reno).
• Fractional Diffusion: Answers and Questions, Probability Seminar, University of Washington, October 2012 (with Boris Baeumer, Department of Mathematics & Statistics, University of Otago, New Zealand; David Benson, Department of Geological Engineering, Colorado School of Mines; Zhen-Qing Chen, Department of Mathematics, University of Washington; Peter Kern, Department of Mathematics, Heinrich Heine University, Duesseldorf, Germany; M. Kovács, Department of Mathematics & Statistics, University of Otago, New Zealand; Erkan Nane, Department of Mathematics and Statistics, Auburn University; Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany; René Schilling, Instiute for Stochastic Mathematics, Technical University of Dresden, Germany; Rina Schumer, Department of Hydrological Sciences, Desert Research Institute, Reno, Nevada; Alla Sikorskii, Department of Statistics and Probability, Michigan State University; Peter Straka, School of Mathematics, University of Manchester, United Kingdom; Stephen W. Wheatcraft, Geological Sciences, University of Nevada, Reno; Yimin Xiao, Department of Statistics and Probability, Michigan State University; and Yong Zhang, Department of Hydrological Sciences, Desert Research Institute, Las Vegas NV).
• The Inverse Stable Subordinator, International Conference on Nonlocal Operators: Analysis, Probability, Geometry and Applications, Center for Interdisciplinary Research (ZiF), University of Bielefeld, Germany, July 2012 (with Boris Baeumer; David Benson; Zhen-Qing Chen; Peter Kern; Erkan Nane; Hans-Peter Scheffler; René Schilling; Rina Schumer; Alla Sikorskii; Peter Straka; Yimin Xiao; and Yuzhen Zhou, Department of Statistics and Probability, Michigan State University).
• Fractional Calculus Models for Anomalous Diffusion, SAMSI summer program on Nonlocal Continuum Models for Diffusion, Mechanics, and Other Applications, Research Triangle Park, North Carolina, 26 June 2012 (with Boris Baeumer; David Benson; Peter Kern; M. Kovács; Eric LaBolle, Land, Air, & Water Resources, U. California, Davis; Jeff Mortensen, Mathematics and Statistics, U. Nevada, Reno; Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii; Peter Straka; Charles Tadjeran, University of Nevada, Reno; Stephen W. Wheatcraft, Geological Sciences, University of Nevada, Reno; and Yong Zhang, Department of Hydrological Sciences, Desert Research Institute, Las Vegas NV).
• Fractional calculus models for medical ultrasound, 4th International Conference on Porous Media, Purdue University, May 14–16, 2012 (with Boris Baeumer; David Benson; James Kelly; Erkan Nane; Peter Kern; Robert McGough; Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii; Peter Straka; Yimin Xiao; and Yuzhen Zhou).
• Continuous Time Random Walks and Fractional Wave Equations, 5th Symposium on Fractional Differentiation and its Applications, Nanjing, China, 14-17 May 2012 (with Peter Straka; Robert McGough; Yuzhen Zhou; Boris Baeumer; David Benson; James Kelly; Erkan Nane; Peter Kern; Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii; and Yimin Xiao).
• 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; Yuzhen Zhou; Robert McGough; Boris Baeumer; David Benson; James Kelly; Erkan Nane; Peter Kern; Hans-Peter Scheffler; Rina Schumer; Alla Sikorskii; and Yimin Xiao).
• 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).

• Extreme value theory with operator norming, Extremes, to appear (with Hans-Peter Scheffler; and Stilian Stoev, Department of Statistics, University of Michigan).
  
• Correlation Structure of Fractional Pearson Diffusions, Computers and Mathematics with Applications, to appear.  Invited contribution to the special issue on Fractional Differentiation and its Applications I (with Nikolai N. Leonenko, Cardiff School of Mathematics, Cardiff University; and Alla Sikorskii, Department of Statistics and Probability, Michigan State University).
  
• A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model, Computers and Mathematics with Applications, to appear in the special issue on Fractional Differentiation and its Applications I (with Hongmei Zhang, School of Mathematical and Computer Sciences, Fuzhou University, China; Fawang Liu, Mathematical Sciences, Queensland University of Technology, Australia; and Mantha S. Phanikumar, Civil and Environmental Engineering, Michigan State University).
• Directional behavior of anomalous diffusion expressed through a multidimensional fractionalization of the Bloch-Torrey equation, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, to appear (with Johnson J. GadElkarim, Department of Electrical and Computer Engineering and Department of Psychiatry, University of Illinois at Chicago; Richard M. Magin, Department of Bioengineering, University of Illinois at Chicago;  Silvia Capuani, Department of Physics, Sapienza University of Rome; Marco Palombo, Department of Physics, Sapienza University of Rome; Anand Kumar, Department of Psychiatry, University of Illinois at Chicago; and Alex D. Leow, Department of Bioengineering, University of Illinois at Chicago).
• Semi-Markov approach to continuous time random walk limit processes (with Peter Straka).
  
• Hydraulic Conductivity Fields: Gaussian or Not? (with Mine Dogan, Remke L. Van Dam, and David W. Hyndman, Department of Geological Sciences, Michigan State University; and David Benson, Department of Geological Engineering, Colorado School of Mines).
  
• Parameter estimation for operator scaling random fields (with Chae Young Lim, Department of Statistics and Probability, Michigan State University; and Hans-Peter Scheffler).
  
• Tempered Fractional Brownian Motion (with Farzad Sabzikar, Department of Statistics and Probability, Michigan State University).
• Reflected stable subordinators and their governing equations, (with Boris Baeumer, Department of Mathematics and Statistics, University of Otago, Dunedin, NZ;  M. Kovács, Department of Mathematics and Statistics, University of Otago, Dunedin, NZ; René L. Schilling, Institute of Mathematical Stochastics, Technical University of Dresden, Germany; and Peter Straka, School of Mathematics, University of Manchester, United Kingdom).
• Attenuated fractional wave equations with anisotropy (with Robert J. McGough, Department of Electrical and Computer Engineering, Michigan State University).