Random perturbations of dynamical systems
Title:
Random perturbations of dynamical systems
Author:
Freĭdlin, M. I. (Mark Iosifovich), author.
ISBN:
9783642258466
Personal Author:
Edition:
Third edition
Physical Description:
xxviii, 458 pages : illustrations ; 25 cm
Series:
Grundlehren der mathematischen Wissenschaften : a series of comprehensive studies in mathematics, 260
Grundlehren der mathematischen Wissenschaften ; 260
General Note:
"The first edition of this book was published in 1979 in Russian"--Pref. to 2nd. ed
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
Abstract:
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
Added Author: