Dynamical systems under the action of fast random perturbations
type: Item
instance of: scholarly article
title: Dynamical systems under the action of fast random perturbations
zbMATH Open document ID: 0733.60081
DOI: 10.1007/BF01066896
published in: Ukrainian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: The author considers dynamical systems of the type \[ dx_{\epsilon}(t)/dt=a(x_{\epsilon}(t),y_{\epsilon}(t)),\quad \epsilon >0. \] The pair \((x_{\epsilon}(t),y_{\epsilon}(t))\) is a Markov process with the infinitesimal operator \[ A_{\epsilon}f(x,y)=(a(x,y),f_ x(x,y))+(1/\epsilon)\int [f(x,y')- f(x,y)]\Pi (x,y,dy'), \] where \(\Pi\) (x,y,\(\cdot)\) is a finite measure. Sufficient conditions are given under which the processes \(x_{\epsilon}(t/\epsilon)\) converge weakly to a certain diffusion process as \(\epsilon\to 0\).
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4213158
zbMATH Keywords: weak convergence
zbMATH Keywords: infinitesimal operator
author: Anatolii V. Skorokhod
reviewed by: Henrikas Pragarauskas
MaRDI profile type: Publication
cites work: Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
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description: scientific article; zbMATH DE number 4213158