This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.

中文翻译：

---

具有跳跃和随机时滞的随机演化方程的平均原理。

本文研究了具有随机和随机时滞的随机演化方程的平均原理，该方程由两个时间尺度的马尔可夫切换过程调制，快速和慢速分量同时存在。我们证明存在一个极限过程（平均方程）比原始过程简单得多。