On invariant measures of stochastic recursions in a critical case

• 成果类型: Article
• 署名作者: Buraczewski, Dariusz
• 署名单位: University of Wroclaw
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000140
• 发表日期: 2007
• 页码: 1245-1272
• 关键词: random walks; asymptotic-behavior; equation

摘要

We consider an autoregressive model on R defined by the recurrence equation X-n = A(n)X(n-1) + B-n, where {(B-n, A(n))} are i.i.d. random variables valued in R x R+ and E[log A(1)] = 0 (critical case). It was proved by Babil-lot, Bougerol and Elie that there exists a unique invariant Radon measure of the process {X-n}. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.