Almost Periodic Solutions and Stable Solutions for Stochastic   Differential Equations
  In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov functions. Under suitable conditions besides Lyapunov functions, we obtain the existence of almost periodic solutions in distribution. 
Yong Li, Zhenxin Liu, and Wenhe Wang
math.DS math.PR