Format:
1 Online-Ressource (xvii, 375 pages)
,
digital, PDF file(s).
ISBN:
9780511760303
Series Statement:
Cambridge tracts in mathematics 182
Content:
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.
Content:
Introduction -- Tools from Markov process theory -- Nonlinear Markov processes and semigroups -- Applications to interating particles
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521111843
Additional Edition:
ISBN 9780521111843
Additional Edition:
Erscheint auch als Kolokolʹcov, Vassilij N., 1959 - Nonlinear Markov processes and kinetic equations Cambridge [u.a.] : Cambridge University Press, 2010 ISBN 0521111846
Additional Edition:
ISBN 9780521111843
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521111843
Language:
English
Subjects:
Mathematics
Keywords:
Markov-Prozess
;
Nichtlinearer Prozess
;
Kinetische Gleichung
DOI:
10.1017/CBO9780511760303
