Random perturbations of dynamical systems
By: M.I. Freidlin, A.D. Wentzell ; translated by Joseph Szücs.
Contributors: Wentzell, Alexander D.; Wentzell, Alexander D.
Edition: 2nd ed.
Series: Grundlehren der mathematischen Wissenschaften ;; 260
Publisher: Springer
Published: 1998
Place of publication: New York
Language: eng
Number of pages: 430
Subjects: Stochastic processes; Perturbation (Mathematics)
Description: This volume is concerned with various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems, especially with the long-time behavior of the perturbed system. In particular, exit problems, metastable states, optimal stabilization, and asymptotics of stationary distributions are also carefully considered.

The authors' main tools are the large deviation theory the centred limit theorem for stochastic processes, and the averaging principle - all presented in great detail. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system.

Most of the results are closely connected with PDEs, and the authors' approach presents a powerful method for studying the asymptotic behavior of the solutions of initial-boundary value problems for corresponding PDEs.
Notes: Includes bibliographical references (p. [417]-427) and index.
"[Based on the] original Russian edition: Fluktuat͡s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ, Nauka : Moscow, 1979"--T.p. verso.