Background
Zabczyk, Jerzy Walter was born on March 29, 1941 in Douai, France. Son of Walter Rajnold and Marta Zabczyk.
(Kolmogorov equations are second order parabolic equations...)
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
http://www.amazon.com/gp/product/3540665455/?tag=2022091-20
(The aim of this book is to give a systematic and self-con...)
The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.
http://www.amazon.com/gp/product/0521059801/?tag=2022091-20
(Now in its second edition, this book gives a systematic a...)
Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.
http://www.amazon.com/gp/product/1107055849/?tag=2022091-20
( Mathematical Control Theory: An Introduction presents, ...)
Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. "Covers a remarkable number of topics....The book presents a large amount of material very well, and its use is highly recommended." --Bulletin of the AMS
http://www.amazon.com/gp/product/0817647325/?tag=2022091-20
(This book is devoted to the asymptotic properties of solu...)
This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; and invariant measures for specific models. The focus is on models of dynamical processes affected by white noise, which are described by partial differential equations such as the reaction-diffusion equations or Navier-Stokes equations. Besides existence and uniqueness questions, the authors pay special attention to the asymptotic behavior of the solutions, to invariant measures and ergodicity. The authors present some of the results found here for the first time. For all whose research interests involve stochastic modeling, dynamical systems, or ergodic theory, this book will be an essential purchase.
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Zabczyk, Jerzy Walter was born on March 29, 1941 in Douai, France. Son of Walter Rajnold and Marta Zabczyk.
Master in Mathematics, Warsaw University, Poland, 1963. Doctor of Philosophy in Mathematics, Higher School Education, Gdansk, Poland, 1969. Habilitation in Mathematics, Polish Academy of Sciences, Warsaw, 1976.
Extraordinary Professor in Mathematics, Polish Academy of Sciences, Warsaw, 1983.
Assistant, lecturer, Warsaw U., 1963-1972; adjunct, dozent, Polish Academy Sciences, 1972-1976, 76-83; deputy director Institute Mathematics Polish Academy Sciences, 1983-1991; extraordinary, ordinary professor, Polish Academy Sciences, 1983-1991, 91-; research fellow, U. Warwick, Coventry, England, 1976-1978, 83-84; also visiting professor, U. Warwick, Coventry, England, 1989; research fellow, U. Montreal, Canada, 1978; senior lecturer, Heriot-Watt U., Edinburgh, Scotland, 1984-1985; visiting professor, University of California at Los Angeles, 1987; visiting professor, Scuola Normale Superiore, Pisa, Italy, 1995.
(Now in its second edition, this book gives a systematic a...)
(The aim of this book is to give a systematic and self-con...)
(The aim of this book is to give a systematic and self-con...)
( Mathematical Control Theory: An Introduction presents, ...)
(This book is devoted to the asymptotic properties of solu...)
(Kolmogorov equations are second order parabolic equations...)
Member Polish Mathematics Society (secretary 1982-1983), American Mathematics Society, Warsaw Science Society.
Married Barbara Koleda, July 7, 1969. Children: Joanna, Pawel.