依状态切换的随机微分方程的几乎自守解

Almost automorphic solutions for stochastic differential equations with state-dependent switching

本文研究依状态切换的随机微分方程解的一种好的常返性:几乎自守性.当该类随机微分方程的系数满足适当的条件时,得到依分布几乎自守解的存在唯一性.同时举例说明,当随机微分方程的系数是几乎自守时,方程可以没有二阶矩意义下的几乎自守解.

This paper concerns a kind of reccurence： Almost automorphy for stochastic differential equations with state-dependent switching. The existence and uniqueness of almost automorphic solutions in distribution are established provided the coefficients satisfy some suitable conditions. We also give an example to illustrate that a stochastic differential equation with almost automorphic coefficients might have no square-mean almost automorphic solution.