An averaging principle for dynamical systems in Hilbert space with Markov random perturbations
type: Item
instance of: scholarly article
title: An averaging principle for dynamical systems in Hilbert space with Markov random perturbations
zbMATH Open document ID: 0856.60066
DOI: 10.1016/0304-4149(95)00066-6
author: Frank Hoppensteadt
author: Anatolii V. Skorokhod
author: Habib Salehi
published in: Stochastic Processes and their Applications
publication date: 1997-02-17T00:00:00Z
review text: It is studied the asymptotic behavior of solutions of differential equations \({dx\over dt}= A(y(t/\varepsilon)) x\), \(x(0)= x_0\), where \(A(y)\), \(y\in Y\), is a family of operators generating semigroups of bounded linear operators in a Hilbert space \(H\), and \(y(t)\) is an ergodic jump Markov process in \(Y\). It is shown the convergence of the process \(x_\varepsilon(t)\), as \(\varepsilon\to 0\), to the nonrandom function \(x(t)\) fulfilling an averaged differential equation. There are proved two theorems, and an application to randomly perturbed partial differential equations with nonrandom initial and boundary conditions is included. It is recommended to those interested in asymptotic behavior of solution and of deviation for perturbed infinite-dimensional systems. The exposition is clear and selfcontained.
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 894789
zbMATH Keywords: dynamical systems in Hilbert space
zbMATH Keywords: averaging principle for Markov perturbations
reviewed by: Constantin Vârsan
MaRDI profile type: Publication
full work available at URL: 0304-4149(95)00066-6
OpenAlex ID: W1972226274
cites work: Q5842075
cites work: Q3721531
cites work: Q5808893
cites work: Asymptotic solutions of linear partial differential equations of first order having random coefficients
cites work: Q3774629
cites work: On Stochastic Processes Defined by Differential Equations with a Small Parameter
cites work: Q5639096
cites work: Stability of regime-switching stochastic differential equations
cites work: Q3876768
cites work: Asymptotic analysis of transport processes
cites work: Q4169502
cites work: Filtrage de diffusions avec conditions frontieres : caracterisation de la densite conditionnelle
cites work: Q3996259
cites work: Q3212958
cites work: Q3777182
cites work: Q5524051
cites work: Q3330236
cites work: Q4693053
description: scientific article; zbMATH DE number 894789