Pseudo almost periodicity for stochastic differential equations in infinite dimensions
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Date
2023-04-10
Authors
Chen, Ye-Jun
Ding, Hui-Sheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Pseudo almost periodic, Solutions in distribution, Stochastic differential equations in infinite dimensions
Citation
Chen, Y. J., & Ding, H. S. (2023). Pseudo almost periodicity for stochastic differential equations in infinite dimensions. <i>Electronic Journal of Differential Equations, 2023</i>(34), pp. 1-14.
Rights
Attribution 4.0 International