Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 34, pp. 1-14.

Title: Pseudo almost periodicity for stochastic differential equations in infinite dimensions
       
Authors: Ye-Jun Chen (Jiangxi Normal Univ., Nanchang, Jiangxi, China)
         Hui-Sheng Ding (Jiangxi Normal Univ., Nanchang, Jiangxi, China)

Abstract:
In this article, we introduce the concept of p-mean θ-pseudo almost periodic
stochastic processes, which is slightly weaker than p-mean pseudo almost
periodic stochastic processes. Using the operator semigroup theory and
stochastic analysis theory, we obtain the existence and uniqueness of square-mean
θ-pseudo almost periodic mild solutions for a semilinear stochastic
differential equation in infinite dimensions. Moreover, we prove that the
obtained solution is also pseudo almost periodic in path distribution.
It is noteworthy that the ergodic part of the obtained solution is not only ergodic
in square-mean but also ergodic in path distribution. Our main results are even new
for the corresponding stochastic differential equations (SDEs) in finite dimensions.

Submitted October 19, 2022. Published April 10, 2023.
Math Subject Classifications: 60H15, 34C27.
Key Words: Pseudo almost periodic; solutions in distribution; 
           stochastic differential equations in infinite dimensions.