Two ergodicity criteria for stochastically recursive sequences
type: Item
instance of: scholarly article
title: Two ergodicity criteria for stochastically recursive sequences
zbMATH Open document ID: 0810.60029
DOI: 10.1007/BF00994261
published in: Acta Applicandae Mathematicae
publication date: 1994-09-28T00:00:00Z
review text: For a stochastically recursive sequence \(X(n+1) = f(X(n), Z(n))\), where \((Z(n))\) is stationary and metrically transitive, criteria for coupling and strong coupling convergence to a stationary sequence are proved. The fundamental property for these theorems to hold is: An event \(A \in \sigma (Z(k) : k = m + n)\) is renovating on the time interval \([n,n + m]\) for \((X(n))\) if \(X(n + m + 1) = g(Z(n), \dots, Z(n + m))\) for some function \(g\) on the set \(A\). The proofs depend on the notion of renovating events and renovating sequences of events, and on the fact that the existence of a stationary sequence of renovating events for \((X(n))\) (with the same \(g)\) is equivalent to strong coupling convergence.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 579594
zbMATH Keywords: coupling
zbMATH Keywords: strong coupling convergence
zbMATH Keywords: stationary sequence
author: A. A. Borovkov
author: Sergey Foss
reviewed by: Hans Daduna
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00994261
OpenAlex ID: W2085729264
description: scientific article; zbMATH DE number 579594