ENGLISH

Nonlinear Markov processes and kinetic equations

By Vassili N. Kolokoltsov

Book information

Publisher
CUP
Year
2010
ISBN
9780521111843, 0521111846
LCC
QA274.7 .K656 2010
Open Library ID
OL25002259M
Language
english
Format
PDF
Filesize
2 MB (1683425 bytes)
Series
Cambridge Tracts in Mathematics
Pages
395\395
Library
Kolxo3
Time added
2010-11-11 16:01:50

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.

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