Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften) - Hardcover

Mark I. Freidlin

Hardcover

ISBN 10: 0387983627 ISBN 13: 9780387983622

Publisher: Springer, 1998

Synopsis

A treatment of various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems. Apart from the long-time behaviour of the perturbed system, exit problems, metastable states, optimal stabilisation, and asymptotics of stationary distributions are considered in detail. The authors'main tools are the large deviation theory, the central limit theorem for stochastic processes, and the averaging principle. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system, and most of these results are closely connected with PDEs. This new edition contains expansions on the averaging principle, a new chapter on random perturbations of Hamiltonian systems, along with new results on fast oscillating perturbations of systems with conservation laws. New sections on wave front propagation in semilinear PDEs and on random perturbations of certain infinite-dimensional dynamical systems have been incorporated into the chapter on sharpenings and generalisations.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Review

Second Edition M.I. Freidlin; A.D. Wentzell; and J. Szücs Random Perturbations of Dynamical Systems "A very detailed and deep mathematical treatment of the long term behavior of randomly perturbed dynamical systems."—ZENTRALBLATT MATH

Edition details

• Publisher: Springer
• Publication date: 1998
• ISBN 10: 0387983627
• ISBN 13: 9780387983622
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 429