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Author Freĭdlin, M. I. (Mark Iosifovich)

Title Random perturbations of dynamical systems / Mark I. Freidlin, Alexander D. Wentzell ; translated by Joseph Szücs
Edition Third edition
Published Heidelberg ; New York : Springer, 2012
Online access available from:
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Description 1 online resource (xxviii, 458 pages) : illustrations
Series Grundlehren der mathematischen Wissenschaften : a series of comprehensive studies in mathematics, 0072-7830 ; 260
Grundlehren der mathematischen Wissenschaften ; 260
Contents Random Perturbations -- Small Random Perturbations on a Finite Time Interval -- Action Functional -- Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point -- Perturbations Leading to Markov Processes -- Markov Perturbations on Large Time Intervals -- The Averaging Principle. Fluctuations in Dynamical Systems with Averaging -- Random Perturbations of Hamiltonian Systems -- The Multidimensional Case -- Stability Under Random Perturbations -- Sharpenings and Generalizations
Summary 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
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
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
Analysis Mathematics
Distribution (Probability theory)
Probability Theory and Stochastic Processes
Bibliography Includes bibliographical references (pages 441-455) and index
Subject Stochastic processes.
Perturbation (Mathematics)
Stochastic Processes.
Form Electronic book
Author Wentzell, Alexander D.
ISBN 1461206111
3642258468 (isbn gedrukte versie)
3642258476 (electronic bk.)
9783642258466 (isbn gedrukte versie)
9783642258473 (electronic bk.)
Other Titles Fluktuat͡sii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ. English