Address: Department of Mathematics, Applied Mathematics and Statistics and
Center for Stochastic and Chaotic Processes
in Science and Technology
Case Western Reserve University
Cleveland, OH 44106
Mazury Lake District, Poland, 2004
U.S. Citizen, married to Liz Holbrook W.; Children: Martin Wojbor W. (37), Gregory Holbrook W. (24), Lauren Pike W. (20)
Wroclaw, Poland, 2011 Prix la Recherche, Laureat Mathematiques, Paris 2013
Key Largo, Florida Bay, 2014 Team USA, Gordon Trophy, London, ON, Canada 2014
Professional and Academic Data
M.Sc. in Electrical and Computer Engineering., Wroclaw University of Technology, 1966
Ph.D. in Mathematics, University of Wroclaw, 1968 (K. Urbanik, advisor)
Habilitation in Mathematics, 1972
Fellow of the Institute of Mathematical Statistics, San Francisco, elected in 1986
Probability theory, Levy
stochastic processes and nonlocal evolution equations,
random fields and their statistics, nonlinear, stochastic
and fractional evolution equations, harmonic and functional analysis, random
graphs, statistical physics and hydrodynamics, chaotic dynamics, applications
to chemistry, physics, operations research, financial mathematics, medicine,
oceanography and atmospheric physics, history of mathematics.
1982-95, Case Western Reserve University, Professor, Department of Mathematics and Statistics
1982-91, Chair, Department of Mathematics and Statistics
1989-present, Director, CWRU Center for Stochastic and Chaotic Processes in Science and Technology
1995-2013, Professor, Department of Statistics
2001-2002, Chair, Department of Statistics
2013-present, Professor, Department of Mathematics, Applied Mathematics and Statistics
Recent Visiting Appointments
1988 University of New South Wales, Sydney (Winter)
1991 Gottingen University (Fall)
1992, 1993, 1994 Nagoya University (Summers)
1994 University of Minnesota, IMA, (Winter and Spring)
1996 Gottingen University (Summer)
1997 Wroclaw University (Spring)
1997 University of Tokyo (Summer)
1998 Princeton University (Fall)
2003 Universite Pierre et Marie Curie, Paris 6
2005 Universite Paris X (Fall)
2009 National Taiwan University, Taipei (Spring)
2009 Ecole Polytechnique,
2010 Ecole Polytechnique,
Recent Editorial Work
2007- present UNIVERSITEXT
, Springer series of graduate textbooks, Series Editor
- Probability -- Winter School (coed. with Z. Ciesielski and K. Urbanik), Springer's Lecture Notes in Math. 472, 1975, 283 pp.
- Martingale Theory in Harmonic Analysis and Banach Spaces (coed. with J.A. Chao), Springer's Lecture Notes in Math. 939, 1982, 225 pp.
- Probability Theory and Harmonic Analysis (coed. with J.A. Chao), Marcel Dekker, Inc. 1986, 291 pp.
- Random Series and Stochastic Integrals: Single and Multiple (with S. Kwapien), Birkhauser-Boston 1992, 360 pp.
- Nonlinear Waves and Weak Turbulence (coed. with N. Fitzmaurice, D. Gurarie and F. McCaughan), Birkhauser-Boston 1993, 345 pp.
- Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence, (coed. with T. Funaki), IMA Volume 77, Springer-Verlag 1996, 312pp.
- Through a Reporter's Eyes: The Life of Stefan Banach, by R. Kaluza. Translated and edited by A. Kostant and W.A. Woyczynski, Birkhauser-Boston 1996, 137pp.
- Distributions in the Physical and Engineering Sciences: Volume 1: Distributional and Fractal Calculus, Integral Transforms, Wavelets, (with A. Saichev), Birkhauser-Boston 1997, 331 pp.
- Stochastic Models in Geosystems, (coed. with S.A. Molchanov), IMA Volume 85, Springer-Verlag, 1997, 487 pp.
- Burgers-KPZ Turbulence. Gottingen Lectures, Springer's Lecture Notes in Math. 1700, 1998, 318 pp.
- Introductory Statistics and Random Phenomena: Uncertainty, Complexity and Chaotic Behavior in Engineering and Science (with M. Denker, and Mathematica Uncertain Virtual Worlds by B. Ycart), Birkhauser-Boston, 1998, 508pp.
- A First Course in Statistics for Signal Analysis, Birkhauser-Boston 2006, 206 pp.
- A First Course in Statistics for Signal Analysis, Second Edition (revised and expanded), Birkhauser-Boston 2011, 261 pp.
- Distributions in the Physical and Engineering Sciences: Volume 2: Linear and Nonlinear Dynamics in Continuous Media, (with A. Saichev), Birkhauser-Boston/Springer 2013, 409 pp.
Recent Papers (1995 - present)
A complete list of publications (1964 - present) is here
1995 - 1999
- A maximum principle for Burgers' equation with unimodal moving average data (with Y. Hu), Probability and Mathematical Statistics, 15(1995), 365-383.
- Hyperbolic asymptotics in Burgers' turbulence and extremal processes (with S. Molchanov and D. Surgailis), Comm. Math. Physics 168(1995), 209-226.
- Relaxation functions in dipolar materials (with A. Weron and K. Weron), J. Stat. Physics 78(1995),1027-1038.
- Limit behavior of quadratic forms of moving averages of i.i.d. random variables and its application to the long range prediction of solutions of the Burgers' equation (with Y.Hu), J. Multivar. Anal., 52(1995)(1), 15-44.
- Large-scale structure of the Universe and asymptotics of Burgers' turbulence with heavy-tailed dependent data (with Y. Hu), in Chaos: The Interplay Between Stochastic and Deterministic Behaviour, Springer's Lecture Notes in Physics, Vol.457(1995), Eds., pp.135-150.
- Gibbs-Cox random fields and Burgers' turbulence (with T. Funaki and D. Surgailis), Ann. Appl. Prob. 5(1995), 461-492.
- Fluctuations of passive scalar concentration with nonzero mean gradient in random velocity fields (with V. Klyatskin), J. Theor. Experim. Physics 81(1995), 770-773.
- Shock density in Burgers' turbulence (with Y. Hu), in Nonlinear Stochastic PDE's: Burgers Turbulence and Hydrodynamic Limit, IMA Volume 77(1996), Springer-Verlag, 157-166.
- Model description of passive tracer density fields in the framework of Burgers' and other related model equations (with A. Saichev), in Nonlinear Stochastic PDE's: Burgers Turbulence and Hydrodynamic Limit, IMA Volumes(1996), Springer-Verlag, 167-196.
- Short-time correlation approximations for diffusing tracers in random velocity fields: a functional approach (with V. Klyatskin and D. Gurarie), in Stochastic Modelling in Physical Oceanography(1996), R. Adler et al., Eds., Birkhauser-Boston, 221-270.
- Mathematics in Stefan Banach's time, in The Life of Stefan Banach by R. Kaluza, Birkhauser Boston(1996), pp.107-115.
- Diffusing passive tracers in random incompressible flows: statistical topography aspects (with V. Klyatskin and D. Gurarie), J. Stat. Physics 84(1996), 797-836.
- Spectral properties of the scaling limit solutions of the Burgers equation with singular data (with N.N. Leonenko and V. Parkhomenko), Random Operators and Stochastic Equations 4(1996), 229-238.
- Density fields in Burgers' and KdV-Burgers' turbulence (with A. Saichev), SIAM J. Appl. Math. 56(1996), 1008-1038.
- Hausdorff dimension of regular points in stochastic Burgers flows with Levy alpha-stable initial data (with A. Janicki), J. Stat. Physics 86(1997), 277-299.
- Evolution of Burgers' turbulence in presence of external forces (with A. Saichev), J. Fluid Mech. 331(1997), 313-343.
- Probability distributions of passive tracers in randomly moving media (with A. Saichev), in Stochastic Models in Geosystems, IMA Volume 85(1997), Springer-Verlag, 359-400.
- Dynamical and statistical characteristics of geophysical fields and waves and related boundary- value problems (with V. Klyatskin), in Stochastic Models in Geosystems, IMA Volume 85(1997), Springer-Verlag, 171-208.
- The large-scale structure of the Universe and quasi-Voronoi tessellation of shock fronts in forced inviscid Burgers' turbulence in Rd (with S. Molchanov and D. Surgailis), Ann. Appl. Prob. 7(1997), 200-228.
- Advection of passive and reactive tracers in multi-dimensional Burgers' velocity field (with A.I. Saichev), Physica D, Nonlinear Phenomena 100(1997), 119-141.
- Computing with Brownian and Levy alpha-stable path integrals, 9th 'Aha Huliko'a Hawaiian Winter Workshop on Monte Carlo Simulations in Oceanography (1997), P. Muller and D. Henderson, Eds., University of Hawaii, 91-100.
- Seeking Birnbaum, Ann. Polish Math. Soc. 33 (100th Anniversary Issue, 1997), 137-155 (in Polish).
- Option pricing bounds in an alpha-stable security market (with A. Janicki, I. Popova, P. Ritchken ), Communications in Statistics--Stochastic Models 13(1997), 817-839.
- Interacting particle approximation for fractal Burgers equation (with T. Funaki), Stochastic Processes and Related Topics - In Memory of Stamatis Cambanis, I. Karatzas, B.S. Rajput and M.S. Taqqu, Eds., (1998) Birkhauser-Boston, pp. 141-168.
- Fractal Burgers equations (with P. Biler and T. Funaki), J. Diff. Equations 148(1998), 9-46.
- Exact parabolic asymptotics for singular n-D Burgers' random fields: Gaussian approximation (with N.N. Leonenko), Stoch. Proc. Appl. 76(1998), 141-166.
- Scaling limits of solutions of the heat equation for singular non-Gaussion data (with N.N. Leonenko), J. Stat. Physics 91(1998), 423-438.
- Parameter estimation of random fields arising in 3-D Burgers' turbulence (with N.N. Leonenko), Functional Analysis V, Proc. Postgraduate School and Conf., Dubrovnik, Croatia, 1997, Butkovic, H. Kraljevic and G. Peskir, Eds., Aarhus University, Various Publications Series No. 44(1998), pp. 61-70.
- Global and exploding solutions for nonlocal quadratic evolution problems (with P. Biler), SIAM J. Appl. Math. 59(1998), 845-859.
- AFM nanoindentation as a method to determine microhardness of hard thin films (with T. Bao and P.W. Morrison), in High-Density Magnetic Recording and Integrated Magneto-Optics , K. Rubin, J.A. Bain and T. Nolan, Eds., Materials Research Society, Pittsburgh, Pa., (1998), pp. 101-106.
- Asymptotics of multifractal conservation laws (with P. Biler and G. Karch), Studia Mathematica 135(1999), 231-252.
- Statistical inference for long-memory random fields arising in Burgers' turbulence (with N.N. Leonenko), Theory of Stochastic Processes 3(1-2)(1999), 55-63.
- Parameter identification for singular random fields (with N.N. Leonenko), J. Statistical Planning and Inference 80(1999), 1-13.
- Interacting particle approximation for nonlocal quadratic evolution problems (with P. Biler and T. Funaki), Probability and Mathematical Statistics, 19.2 (1999), 267-286.
2000 - 2004
- Nonlocal quadratic evolution problems (with P. Biler), in Evolution Equations, Banach Center Publications (Warsaw) 52(2000), 11-24.
- Multifractal and Levy conservation laws (with P. Biler and G. Karch), Comptes Rendus, Acad. Sci (Paris), 330(5)(2000), 343-348.
- Relative molecular diffusion (with E.Z. Gribova, I.S. Zhukova and A.I. Saichev), Radiophysics and Quantum Electronics, 43.4 (2000), 411-421.
- Nonlinear diffusion approximations of queuing networks (with B. Margolius), in Stochastics in Finite and Infinite Dimensions, In Honor of Gopinath Kallianpur, T. Hida, R.L. Karandikar, H. Kunita, B.R. Rajput, S. Watanabe and J. Xiong, Eds., (2001) Birkhauser-Boston, 259-284.
- A story of a painting, Mathematical Intelligencer 23(1)(2001), 39.
- Seeking Birnbaum, or nine lives of a mathematician, Mathematical Intelligencer 23(2)(2001), 36-46.
- Growing fractal interfaces in the presence of self-similar hopping surface diffusion (with J.A. Mann), Physica A. Statistical Mechanics and Its Applications, 291(2001), 159-183.
- Passive tracer transport in stochastic flows, in Stochastic Climate Models, L. Arnold, P. Imkeller, P. Mueller, Eds., Progress in Probability, Vol. 49(2001), Birkhauser-Basel, 385-398. (Chorin) (Picture)
- Levy processes in the physical sciences, in Levy Processes - Theory and Applications, T. Mikosch, O. Barndorff-Nielsen, S. Resnick, Eds., (2001)Birkhauser-Boston, 241-266.
- Asymptotics and high-dimensional approximations for nonlinear pseudodifferential equations involving Levy generators (with P. Biler and G. Karch), Demonstratio Mathematica 34(2001), 403-413.
- Kazimierz Urbanik and his research (with Z. Jurek and J. Rosinski), Demonstratio Mathematica 34(2001), 219-239.
- Critical nonlinearity exponent and self-similar asymptotics for Levy conservation laws (with P. Biler and G. Karch), Annales d'Institute H. Poincare - Analyse Nonlineaire, (Paris) 18(2001), 613-637.
- Parameter identification for stochastic Burgers' flows via parabolic rescaling (with N. Leonenko), Probability and Mathematical Statistics, 21.1 (2001), 1-55.
- Asymptotics for conservation laws involving Levy diffusion operators (with P. Biler and G. Karch), Studia Mathematica 148(2001), 171-192.
- Limit theorems for the Burgers equation initialized by data with long-range dependence (with D. Surgailis), in Stochastic Processes with Long Range Dependence, P. Doukhan, G. Oppenheim and M. Taqqu, Ed., Birkhauser-Boston, 2003, pp. 507-524.
- Length of sums in a Minkowski space (with G.O.H. Katona and R. Mayer), in Towards a Theory of Geometric Graphs, J. Pach, Ed., Contemporary Mathematics Series, American Mathematical Society, Providence, R.I., 2003, pp. 77-83.
- Distributions of suprema of Levy processes via the Heavy Traffic Invariance Principle (with W. Szczotka), Probability and Mathematical Statistics, 23.2 (2003), 251-272.
2005 - 2009
- Nonlinear partial differential equations driven by Levy diffusions and related statistical issues, in Probability and Partial Differential Equations in Modern Applied Mathematics, J. Duan and E.C. Waymire, Eds. IMA Volumes, Springer-Verlag, IMA Volume 140, pp. 247-258
- Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws (with B. Jourdain and S. Meleard), Bernoulli, 11(2005), 689-714.
- Models of anamalous diffusion:The subdiffusive case (with A. Piryatinska and A.I.Saichev), Physica A: Statistical Physics, 349(2005), 375-424.
- Notes on fractional Ornstein-Uhlenbeck random sheets (with Gy. Terdik), Publicationes Mathematicae, 66(2005), 153-181.
- A probabilistic approach for nonlinear equations involving fractional Laplacian and singular operator (with B. Jourdain and S. Meleard), Potential Analysis, 23.1 (2005), 55-81.
- Parametric optimization of microhardness of diamondlike carbon films prepared by plasma enhanced chemical vapor deposition (with T. Bao and P.W. Morrison, Jr.), Thin Solid Films, 485(2005), 27-41.
- Numerical study of interacting particles approximation for integro-differential equations (with D. Stanescu and D. Kim), Journal of Computational Physics, 206(2005), 706-726.
- Kazimierz Urbanik (1930-2005) (with Z. Jurek and J. Rosinski), Probability and Mathematical Statistics, 25.1 (2005), 1-22.
- Are Levy flights multiscale? (with Gy. Terdik and A. Piryatinska), Pure Mathematics and Applications, 15 (2005), 323-333.
- Fractional- and integer-order moments, and multiscaling for smoothly truncated Levy flights (with Gy. Terdik and A. Piryatinska), Physics Letters A, 348 (2006), 94-109.
- Rosinski Measures for Tempered Stable and Related Ornstein-Uhlenbeck Processes (with Gy. Terdik), Probability and Mathematical Statistics, 26.2 (2006), 213-243.
- Generalized solutions of nonlinear parabolic equations and diffusion processes (with Ya. Belopolskaya), Acta Applicandae Mathematicae, 96 (2007), 55-69.
- General nonlocal diffusion-convection mean field models: nonexistence of global solutions (with P. Biler), Physica A: Statistical Mechanics and Applications, 379 (2007), 523-533.
- Critical exponents for large time asymptotics for fractal Hamilton-Jacobi-KPZ equations (with G. Karch), Proceedings in Applied Mathematics and Mechanics (PAMM), 7 (2008), 205-206.
- Fractal Hamilton-Jacobi-KPZ equations, (with G. Karch), Transactions of the American Mathematical Society, 360 (2008), 2423-2442.
- Nonlinear stochastic differential equations driven by Levy processes and related partial differential equations, (with B. Jourdain and S. Meleard), ALEA- Latin American Journal on Probability and Mathematical Statistics, 4 (2008), 1-29.
- Automated detection of neonate EEG sleep stages (with A. Piryatinska, G. Terdik, K. Loparo, M. Scher, A. Zlotnik), Computer Methods and Algorithms in Biomedicine, 95 (2009), 31-46.
2010 - 2015
- Parametric estimation for fractional Poisson processes (with V Uchaykin and D. Cahoy), Journal of Statistical Planning and Inference, 140 (2010), 3106-3120.
- Random local temporal structure of category fluency responses (with David Meyer, Jason Messer, Tanya Singh, Peter J. Thomas, Jeffrey Kaye, M.D., and Alan J. Lerner M.D.), Journal of Computational Neuroscience 32 (2011), 213-231.
- Optimal channel selection for analysis of EEG-sleep patterns in neonates (with A. Piryatinska, K. Loparo and M. Scher), Computer Methods and Algorithms in Biomedicine, 106 (2012), 14-26.
- Generalized solutions of the Cauchy problem for systems of nonlinear parabolic equations and diffusion processes (with Ya. Belopolskaya), Stochastics and Dynamics, 12 (2012), 1-31.
- Probabilistic approach to construction of viscosity solutions for the Cauchy problem for systems of fully nonlinear parabolic equations (with Y. Belopolskaya), Proceedings of the Seminar of the St. Petersburg Division of the Mathematical Institute of Russian Academy of Sciences, 396 (2012), 31-66.
- The legend of Hugo Steinhaus:tales of two cities, up close and personal, Annals of the Polish Mathematical Society (Wiadomosci Matematyczne), 6th European Congress of Mathematics Issue, 48 (2012), 293-311.
- Levy flights in evolutionary ecology (with S. Meleard and B. Jourdain), Journal of Mathematical Biology 65 (4) (2012), 677-707.
- A lost opportunity: Recovering the end of Major League Baseball's 1994 strike shortened season (with Z. Hass, C. Yanosko, and Eric Becker), Mathematica Applicanda 40 (2) (2012), 13-31.
- Levy processes as heavy traffic limits of tandem queues with heavy tails (with M. Czystolowski, and W. Szczotka), Probability and Mathematical Statistics, 33 (2013), 107-120.
- SDES, FBSDES and fully nonlinear parabolic systems (with Y. Belopolskaya), Rendiconti del Seminario Matematico, Universita e Politecnico di Torino, 71(2) (2013), 209-218.
- Multiscale conservation laws driven by L\'evy stable and Linnik diffusions: Asymptotics, shock creation, preservation and dissolution (with B. Gunaratnam), Journal of Statistical Physics 160(2015), 29-59.
- William Feller: A Biography (with R. Schilling), in Selected Works of William Feller, Volume 1, Springer-Verlag 2014/2015, pp. 17-40.
- Within-generation bet hedging can be selected for even in large, panmictic populations (with R. Snyder and S. Burgess ), The American Naturalist (2015), 23 pages.
- Rough Paths and Regularity Structures. Martin Hairer's 2014 Fields Medal, Annals of the Polish Mathematical Society (Wiadomosci Matematyczne) (invited paper), (2015), 1-6 (in Polish).
- Explicit representation for multiscale Levy processes, and asymptotics of multifractal conservation laws (with K. Gorska), Journal of Mathematical Physics (2015), 25 pages.
Graduate Students and their present affiliations:
Jan Rosinski (Professor, Dept. of Mathematics, University of Tennessee, Knoxville, TN),
Jerzy Szulga (Professor, Dept. of Mathematics, Auburn University, Auburn, AL),
Marek Musiela (Professor, Oxford-Man Institute of Quantitative Finance, Oxford University, U.K.),
Volker Schmidt ( Professor, Institut fur Stochastik, Ulm University, Ulm, Germany),
Eric Rains (Professor, Dept. of Mathematics, California Institute of Technology, Pasadena, CA),
Barbara Margolius (Associate Professor, Dept. of Mathematics, Cleveland State University, Cleveland, OH),
Zbigniew Suchanecki (Researcher, Solvay Institute, Bruxelles, Belgium),
Bohdan Aniszczyk (Education Commissioner, City Council, Wroclaw, Poland),
Maria Aniszczyk (Sr. Lecturer, Institute of Mathematics, Wroclaw University of Technology, Wroclaw, Poland),
S. Sniezka (Professor, Institute of Mathematics, Vilnius University, Vilnius, Lithuania),
K. Kobryn, (Sr. Lecturer, Dept. of Mathematics, Wroclaw Institute of Agriculture, Wroclaw, Poland),
W. Wawrzyniak (Sr. Lecturer, Instiute of Mathematics, Wroclaw University of Technology, Wroclaw, Poland),
Yiming Hu (Analyst, Bank of America, Swap Trade Desk Technology Support Group, Chicago, IL),
Pingfu Fu (Associate Professor, Epidemiology and Biostatistics, Case Western Reserve U., Cleveland, OH),
Tim Bao (Manager/Senior Scientist, BTU International, Cambridge, MA/Shanghai, China),
Brian Schmotzer (Senior Researcher, Center for Clinical Investigation, Case Western Reserve U.),
Neepa Subramanian (Manager, Progressive Corporation, Cleveland, Ohio),
Sreenivas Konda (Assistant Professor, Department of Statistics, University of California, Santa Barbara, CA)
Alexandra Piryatinska (Associate Professor, Dept. of Mathematics, San Francisco State University, CA)
Erin McCarthy (Analyst, Hamot Medical Center, Erie, PA)
Connor LeBlanc (Boston, MA)
Dexter Cahoy (Associate Professor, Dept. of Mathematics, Louisiana Tech University, Ruston, LA)
Brian A. Geier (Broad Institute of MIT and Harvard, Cambridge, MA)
Amy R. Orendi (Pittsburgh, PA)
Julie Tutlys (Analyst, Humedica, Boston, MA)
Peipei Shi (Researcher, Eli Lilly, Inc., Indianapolis, IN)
Quansheng Xi (Case Western Reserve University Medical School, Cleveland, OH)
Catherine Dinda (Mentor, OH)
Alexandru C. Belu (Analyst, Bloomberg, Inc, New York, NY)
Bakeerathan Gunaratnam (Postdoctoral Scholar, Bioinformatics and Biostatistics, U of Louisville, KY)
Tennis, sailing, skiing, music, collecting old books
Copper Mountain, CO, 2008 Mazury Lakes, Poland, 2004
Breckenridge, Colorado, 2015 U.S. National Father-Daughter
Championship, Jupiter, FL, 2014
Fiesta Bowl National
Championship, Scottsdale, AZ, 2014
U.S. National Team Championship,
MIssion Hills, CA, 2007