Nonlinear Markov Processes and Kinetic Equations

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.

Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
Published: 09/06/2010
Pages: 375
Binding Type: Hardcover
Weight: 1.49lbs
Size: 9.00h x 6.00w x 1.10d
ISBN: 9780521111843

About the Author
Kolokoltsov, Vassili N.: - Vassili N. Kolokoltsov is a Reader in Probability in the Department of Statistics at the University of Warwick.