Algebraic criteria and sufficient conditions for asymptotic stability and boundedness with probability 1 for the solutions of a system of linear stochastic difference equations
type: Item
instance of: scholarly article
title: Algebraic criteria and sufficient conditions for asymptotic stability and boundedness with probability 1 for the solutions of a system of linear stochastic difference equations
zbMATH Open document ID: 0632.60055
DOI: 10.1007/BF01057295
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: A criterion and sufficient conditions are given for asymptotic stability and boundedness with probability 1 of solutions of a system of linear stochastic difference equations of the form \[ x(k+1)=Ax(k)+\sum^{r}_{i=1}B_ i(\epsilon)x(k)z_ i(k),\quad k=0,1,2,..., \] \[ z_ i(k)=w_ i(k+1)-w_ i(k),\quad i=1,2,...,r, \] where A and \(B_ i(\epsilon)\) are constant \(n\times n\) matrices, w is an \(R^ r\)-valued Wiener process and \(\epsilon\) is a parameter.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 4028541
zbMATH Keywords: asymptotic stability
zbMATH Keywords: linear stochastic difference equations
author: D. G. Korenivs'kyj
MaRDI profile type: Publication
cites work: Q3756245
cites work: Q3700677
cites work: Stability and positive supermartingales
description: scientific article; zbMATH DE number 4028541