Description 
1 online resource (xxviii, 458 pages) : illustrations 
Series 
Grundlehren der mathematischen Wissenschaften : a series of comprehensive studies in mathematics, 00727830 ; 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 initialboundary 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 longtime 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 441455) and index 
Subject 
Stochastic processes.


Perturbation (Mathematics)


Mathematics.


Probability.


Stochastic Processes.

Form 
Electronic book

Author 
Wentzell, Alexander D.

ISBN 
1461206111 

3642258468 (isbn gedrukte versie) 

3642258476 (electronic bk.) 

9781461206118 

9783642258466 (isbn gedrukte versie) 

9783642258473 (electronic bk.) 
