A GENERALIZED BACKWARD SCHEME FOR SOLVING NONMONOTONIC STOCHASTIC RECURSIONS

• 成果类型: Article
• 署名作者: Moyal, P.
• 署名单位: Universite de Technologie de Compiegne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1004
• 发表日期: 2015
• 页码: 582-599
• 关键词: Ergodicity; QUEUE

摘要

We propose an explicit construction of a stationary solution for a stochastic recursion of the form X o theta = phi(X) on a partially-ordered Polish space, when the monotonicity of phi is not assumed. Under certain conditions, we show that an extension of the original probability space exists, on which a solution is well defined, and construct explicitly this extension using a randomized contraction technique. We then provide conditions for the existence of a solution on the original space. We finally apply these results to the stability study of two nonmonotonic queuing systems.