Limit theorems on the convergence of infinite products for parametric stochastic operator systems
type: Item
instance of: scholarly article
title: Limit theorems on the convergence of infinite products for parametric stochastic operator systems
zbMATH Open document ID: 0705.60054
DOI: 10.1007/BF01056272
author: G. P. Butsan
author: M. Yu. Kozachenko
published in: Ukrainian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: This is the fourth of a series of articles by these two authors in this journal. Let \(G_ 2(H)\) consist of all operators of the form \(I+A\) where I is the identity and A is a Hilbert-Schmidt operator on a Hilbert space H. Let \(\{\) Z(t,s): \(0\leq s\leq t\leq T\}\) be a family of \(G_ 2(H)\)- valued random variables. For \(\Delta =\{s=t_ 0<t_ 1<...<t_ n=t\}\), a partition of [s,t]\(\subseteq [0,T]\), let \(X_{\Delta}\) be the ordered product \(\prod^{n}_{i=1}Z(t_ i,t_{i-1}).\) It is shown that in some cases the limit X(t,s) of \(X_{\Delta}\) (as \(\max_{i}(t_ i-t_{i-1})\to 0)\) exists in a certain sense. Properties of the limit process \(\{\) X(t,s)\(\}\) are studied.
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4157613
zbMATH Keywords: infinite products
zbMATH Keywords: Hilbert-Schmidt operator
zbMATH Keywords: Properties of the limit process
reviewed by: Jerome A. Goldstein
MaRDI profile type: Publication
cites work: Limit theorem for parametric stochastic operator systems
cites work: Averaging principle and periodic solutions of a parabolic equation with retarded argument
cites work: Q3695513
cites work: Question of the mixed product of dependent multiplicative semigroups
description: scientific article; zbMATH DE number 4157613