论文标题
随机的周期性解决方案，用于随机微分方程，具有不均匀的消散性
Random periodic solutions for stochastic differential equations with non-uniform dissipativity
论文作者
论文摘要
本文涉及随机微分方程（SDE）的随机周期性解决方案的存在和唯一性，其中所涉及的漂移项不必统一地消失。一方面，通过反射耦合方法，我们研究了没有内存的SDE的分布意义上的随机周期性解决方案的存在，而在长距离长距离漂移仅是耗散的。另一方面，通过同步耦合策略，我们分别建立了具有有限时间滞后和无限时间滞后的功能性SDE的路径随机周期溶液的存在，其中漂移仅平均消散而不是均匀地耗散时间参数。
This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection coupling approach, we investigate the existence of random periodic solutions in the sense of distribution for SDEs without memory, where the drifts are merely dissipative at long distance. On the other hand, via the synchronous coupling strategy, we establish respectively the existence of pathwise random periodic solutions for functional SDEs with a finite time lag and an infinite time lag, in which the drifts are only dissipative on average rather than uniformly dissipative with respect to the time parameters.
