Borkar-Meyn定理的递归包含扩展
A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions
AI总结：
本文扩展了Borkar-Meyn定理，以涵盖均场为微分包含的情况，提出了两种充分条件保证递归包含的稳定性和收敛性，并讨论了近似漂移问题的解法。
摘要：
本文将Borkar和Meyn的稳定性定理扩展到均场为微分包含的情况。提出了两种不同的充分条件，保证了随机递归包含的稳定性和收敛性。本文的工作借鉴了Benaim、Hofbauer、Sorin以及Borkar和Meyn的研究。作为主要定理的一个推论，Borkar和Meyn定理的自然推广得以得出。此外，Borkar和Meyn的原始定理在略微放松的假设下也成立。最后，作为主要定理的应用，我们讨论了近似漂移问题的解法。
英文摘要：
In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion. 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. Finally, as an application to one of the main theorems we discuss a solution to the approximate drift problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
