
Nonlinear Markov Processes and Kinetic Equations
Vassili N. Kolokoltsov(Author)
Cambridge University Press
Published on 15. July 2010
Book
Hardback
394 pages
978-0-521-11184-3 (ISBN)
Description
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Reviews / Votes
'This monograph is suitable for graduate students and researchers who have a good background in probability theory and analysis and have mastered such key topics as martingales, stochastic calculus and weak convergence, on the one hand, and the analytic theory of semigroups, on the other hand. ... This book is pioneering in developing a new and important type of dynamics for modelling complex stochastic systems. It deserves to be widely read.' Bulletin of the London Mathematical Society '... this is an important book. Written with great care by a leading expert, it is accessible to researchers and graduate students in stochastic and functional analysis, with applications in mathematical physics and systems biology.' Mathematical ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 26 mm
Weight
720 gr
ISBN-13
978-0-521-11184-3 (9780521111843)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Vassili N. Kolokoltsov
Nonlinear Markov Processes and Kinetic Equations
E-Book
07/2010
1st Edition
Cambridge University Press
€79.99
Available for download
Person
Vassili N. Kolokoltsov is a Reader in Probability in the Department of Statistics at the University of Warwick.
Content
Preface; Basic notations; 1. Introduction; Part I. Tools From Markov Processes: 2. Probability and analysis; 3. Probabilistic constructions; 4. Analytic constructions; 5. Unbounded coefficients; Part II. Nonlinear Markov Processes and Semigroups: 6. Integral generators; 7. Generators of Levy-Khintchine type; 8. Smoothness with respect to initial data; Part III. Applications to Interacting Particles: 9. The dynamic law of large numbers; 10. The dynamic central limit theorem; 11. Developments and comments; 12. Appendices; References; Index.