JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 113-126.doi: 10.6040/j.issn.1671-9352.0.2022.486

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θ-almost periodic solutions for stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficients

Yejun CHEN1(),Huisheng DING1,2,*()   

  1. 1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, Jiangxi, China
    2. Jiangxi Provincial Center for Applied Mathematics, Nanchang 330022, Jiangxi, China
  • Received:2022-09-09 Online:2023-06-20 Published:2023-05-23
  • Contact: Huisheng DING E-mail:chenyejun999@jxnu.edu.cn;dinghs@mail.ustc.edu.cn

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Abstract:

Based on the work of Raynaud de Fitte, in this paper, we consider almost periodicity of stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficientsUnder the weaker conditions (C0-semigroup generated by A is not necessarily contractive, and F, G can be Stepanov almost periodic and not necessarily almost periodic), we obtain the existence and uniqueness of θ-almost periodic solutions of these equations, and furthermore, we prove that the solution is almost periodic in path distribution.

Key words: almost periodic, θ-almost periodic, Stepanov almost periodic, in distribution, stochastic differential equations

CLC Number: 

  • O211.63
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