带有Stepanov概周期系数的无穷维随机微分方程的θ-概周期解  

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

作　　者：陈叶君 丁惠生[1,2] CHEN Yejun;DING Huisheng(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,Jiangxi,China;Jiangxi Provincial Center for Applied Mathematics,Nanchang 330022,Jiangxi,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]江西省应用数学中心,江西南昌330022

出　　处：《山东大学学报（理学版）》2023年第6期113-126,共14页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11861037);江西省双千计划(jxsq2019201001);江西省教育厅研究生创新基金(YC2021-B078)资助。

摘　　要：基于Raynaud de Fitte的最新工作,本文考虑了带有Stepanov概周期系数的无穷维随机微分方程dX(t)=AX(t)dt+F(t,X(t))dt+G(t,X(t))dW(t)的概周期性。在更弱的条件下(A生成的C0半群不必是压缩的,F、G是Stepanov概周期而不必是概周期的),我们得到了该方程的θ-概周期解的存在性和唯一性,并且证明了该解是依路径分布概周期的。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 coefficients dX(t)=AX(t)dt+F(t,X(t))dt+G(t,X(t))dW(t).Under the weaker conditions(C_0-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 ofθ-almost periodic solutions of these equations,and furthermore,we prove that the solution is almost periodic in path distribution.

关 键 词：概周期 θ-概周期 Stepanov概周期 依分布 随机微分方程 

分 类 号：O211.63[理学—概率论与数理统计]