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E-mail Message: I thought you might be interested in this item at http://www.worldcat.org/oclc/38409445 Title: Random perturbations of dynamical systems Author: M I Freĭdlin; Alexander D Wentzell Publisher: New York : Springer, ©1998. ISBN/ISSN: 0387983627 9780387983622 OCLC:38409445

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Random perturbations of dynamical systems

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Random perturbations of dynamical systems

Author:	M I Freĭdlin; Alexander D Wentzell
Publisher:	New York : Springer, ©1998.
Series:	Grundlehren der mathematischen Wissenschaften, 260
Edition/Format:	Book : English : 2nd edView all editions and formats
Summary:	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 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. Read more...
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Material Type:	Internet resource
Document Type:	Book, Internet Resource
All Authors / Contributors:	M I Freĭdlin; Alexander D Wentzell Find more information about:
ISBN:	0387983627 9780387983622
OCLC Number:	38409445
Notes:	"[Based on the] original Russian edition: Fluktuat︠s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ, Nauka : Moscow, 1979"--T.p. verso.
Description:	xi, 430 p. : ill. ; 24 cm.
Contents:	Ch. 1. Random Perturbations -- Ch. 2. Small Random Perturbations on a Finite Time Interval -- Ch. 3. Action Functional -- Ch. 4. Gaussian Perturbations of Dynamical Systems: Neighborhood of an Equilibrium Point -- Ch. 5. Perturbations Leading to Markov Processes -- Ch. 6. Markov Perturbations on Large Time Intervals -- Ch. 7. The Averaging Principle. Fluctuations in Dynamical Systems with Averaging -- Ch. 8. Random Perturbations of Hamiltonian Systems -- Ch. 9. Stability Under Random Perturbations -- Ch. 10. Sharpenings and Generalizations.
Series Title:	Grundlehren der mathematischen Wissenschaften, 260
Responsibility:	M.I. Freidlin, A.D. Wentzell ; translated by Joseph Szücs.
More information:	Publisher description Table of contents only

Abstract:

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.

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