Wojbor A. WOYCZYNSKI

Address: Department of Statistics and the
Center for Stochastic and Chaotic Processes in Science and Technology
Case Western Reserve University,
Cleveland, OH
44106

phone: 216-368-6941
fax: 216-368-0252
email: waw(at)case.edu

Mazury Lake District, Poland, 2004

Personal Data

U.S. Citizen, married to Liz Holbrook; children: Martin Wojbor (31), Gregory Holbrook (18), Lauren Pike (13)

Professional and Academic Data

Education
M.Sc. E.E., Wroclaw University of Technology, 1966
Ph.D. in Mathematics, Wroclaw University, 1968 (K. Urbanik, advisor)
Habilitation, 1972

Research Interests

Probability theory, Levy stochastic processes, 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.

Recent Appointments

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-present, Professor, Department of Statistics
2001-2002, Chair, Department of Statistics [1] [1]

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 (Summer)
2005 Universite Paris X (Fall)

Recent Editorial Work:

• Probability and Mathematical Statistics, Editorial Board Member, 1988-present; Managing Editor, 2005 - present

• Annals of Applied Probability, Associate Editor, 1989-1996

• Stochastic Processes and Their Applications, Editorial Board Member, 1992-1999

• Applicationes Mathematicae, Associate Editor, 2002-present

Recent Publications:

A complete list of publications is here.

Books:

• Random Series and Stochastic Integrals: Single and Multiple (with S. Kwapien),
  Birkhauser-Boston 1992, 357 pp., second edition in preparation.

• 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.

Other Publications:

1995

• 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), 701-735.

• Fluctuations of passive scalar concentration with nonzero mean gradient in random velocity fields (with V. Klyatskin), J. Theor. Experim. Physics 81(1995), 770-773.

1996

• 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, 221270. 

• 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.

1997

• Hausdorff dimension of regular points in stochastic Burgers flows with Lévy 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 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.

• Option pricing bounds in an alpha-stable security market (with A. Janicki, I. Popova, P. Ritchken ), Comm. Stat.-Stochastic Models 13(1997), 817-839.

1998

• 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.

1999

• 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

• Nonlocal quadratic evolution problems (with P. Biler), in Evolution Equations, Banach Center Publications (Warsaw) 52(2000), 11-24.

• Multifractal and Lévy 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.

2001

• 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.

2002

• Rotation of particles in polarized Brownian flows (with C. Zirbel), Stochastics and Dynamics 2(2002), 109-129.

• Fokker-Planck equations and conservation laws involving Levy diffusion generators (with P. Biler and G. Karch), Miniproc. 2nd Levy Conference on Stochastic Processes and Appl., MaPhySto, Aarhus University, (2002) 64-69.

2003

• 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 Mathematican 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.

2004

• Heavy-tailed dependent queues in heavy traffic (with W. Szczotka), Probability and Mathematical Statistics,  24.1 (2004), 67-96.

2005

• 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.

2006

• 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.

• RosiÅ„ski Measures for Tempered Stable and Related Ornstein-Uhlenbeck Processes (with Gy. Terdik), Probability and Mathematical Statistics, 26.2 (2006), 213-243.

2007

• 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, October 2007, 1-2.

2008

• Fractal Hamilton-Jacobi-KPZ equations, (with G. Karch), Transactions of the Americal Mathematical Society, {\bf 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.

Graduate Students and their present affiliations:

Jan Rosinski (University of Tennessee, Knoxville, TN),
Jerzy Szulga (Auburn University, Auburn, AL),
Zbigniew Suchanecki (Solvay Institute, Bruxelles, Belgium),
B. Aniszczyk (Wroclaw University of Technology, Wroclaw, Poland),
Volker Schmidt (Ulm University, Ulm, Germany),
M. Aniszczyk (Wroclaw University of Technology, Wroclaw, Poland),
S. Sniezka (Vilnius University, Vilnius, Lithuania),
K. Kobryn, (Wroclaw Institute of Agriculture, Wroclaw, Poland),
W. Wawrzyniak (Wroclaw Institute of Agriculture, Wroclaw, Poland),
Marek Musiela (U of New South Wales, Sydney, Australia, and BNP Paribas Financial Modeling Group, London, UK),
Yiming Hu (Bank of America, Swap Trade Desk Technology Support Group, Chicago, IL),
Eric Rains (AT&T Labs),
Barbara Margolius (Cleveland State U),
Pingfu Fu (Epidemiology and Biostatistics, CWRU),
Tim Bao (Motorola Corp., Austin, TX),
Brian Schmotzer (Biostatistics, Emory University, Atlanta, Georgia),
Neepa Subramanian (Progressive Corporation, Cleveland, Ohio),
Sreenivas Konda (Temple University, Philadelphia, PA)
Alexandra Piryatinska (San Francisco State University)
Erin McCarthy (Hamot Medical Center, Erie, PA)
Connor LeBlanc
Dexter Cahoy (Louisiana Tech University, Ruston, LA)

Hobbies:

Tennis, sailing, skiing, music, collecting old books