TY  - BOOK
AU  - Kolokolʹt︠s︡ov,V.N.
TI  - Nonlinear Markov processes and kinetic equations
T2  - Cambridge tracts in mathematics
SN  - 9780511760303 (ebook)
AV  - QA274.7 .K656 2010
U1  - 519.233 22
PY  - 2010///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Markov processes
KW  - Nonlinear theories
KW  - Kinetic theory of matter
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Introduction -- Tools from Markov process theory -- Nonlinear Markov processes and semigroups -- Applications to interating particles
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511760303
ER  -