论文标题
平均两个时间尺度制度的原理
Averaging principle for two time-scale regime-switching processes
论文作者
论文摘要
这项工作研究了一个完全耦合的两个时间尺度系统的平均原理，该系统的缓慢是扩散过程，快速过程是无限可计数状态空间上纯粹的跳跃过程。快速过程的奇迹性对极限系统和平均原理具有重要影响。我们表明，在强烈的偏僻条件下，极限系统接收了独特的解决方案，而L1-norm中的缓慢过程会收敛到极限系统。但是，在某些较弱的长期条件下，极限系统可以接受解决方案，但不一定是唯一的，并且可以证明缓慢的过程弱收敛到极限系统的解决方案。
This work studies the averaging principle for a fully coupled two time-scale system, whose slow process is a diffusion process and fast process is a purely jumping process on an infinitely countable state space. The ergodicity of the fast process has important impact on the limit system and the averaging principle. We showed that under strongly ergodic condition, the limit system admits a unique solution, and the slow process converges in the L1-norm to the limit system. However, under certain weaker ergodicity condition, the limit system admits a solution, but not necessarily unique, and the slow process can be proved to converge weakly to a solution of the limit system.
