Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (2): 341-354.

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Asymptotically Almost Periodic Solutions for Stochastic Differential Equations in Infinite Dimensions

Chen Yejun(),Ding Huisheng()   

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
  • Received:2022-06-22 Revised:2022-10-17 Online:2023-04-26 Published:2023-04-17
  • Supported by:
    NSFC(11861037);Double Thousand Plan of Jiangxi Province(jxsq2019201001);Graduate Innovation Fund of Jiangxi Provincial Education Department(YC2021-B078)

Abstract:

In this paper, we introduce the notion of asymptotically $\theta$-almost periodic stochastic process and study a class of stochastic differential matrixs in infinite dimensions with asymptotically almost periodic coefficients under the framework of operator semigroup theory. Using stochastic analysis theory, the existence of asymptotically $\theta$-almost periodic solutions of these matrixs is established. In addition, the concept of asymptotically almost periodic process in path distribution is introduced, and we prove that the above solutions are also asymptotically almost periodic in path distribution. It is noteworthy that all the earlier related results only give the existence of asymptotically almost periodic solutions in one-dimensional distribution, which are weaker than asymptotically almost periodic solutions in path distribution.

Key words: Asymptotically almost periodic in path distribution, Asymptotically $\theta$-almost periodic, Stochastic differential matrixs

CLC Number: 

  • O211.63
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