A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions

• 成果类型: Article
• 署名作者: Ramaswamy, Arunselvan; Bhatnagar, Shalabh
• 署名单位: Indian Institute of Science (IISC) - Bangalore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0821
• 发表日期: 2017
• 页码: 648-661
• 关键词: Approximation

摘要

In this paper, the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a set-valued map. Two different sets of sufficient conditions are presented that guarantee the stability and convergence of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofbauer and Sorin as well as Borkar and Meyn. As a corollary to one of the main theorems, a natural generalization of the Borkar and Meyn theorem follows. In addition, the original theorem of Borkar and Meyn is shown to hold under slightly relaxed assumptions. As an application to one of the main theorems, we discuss a solution to the approximate drift problem. Finally, we analyze the stochastic gradient algorithm with constant-error gradient estimators as yet another application of our main result.