Asymptotic behavior of stochastic functional differential evolution equation

Electronic Journal of Differential Equations

article

Jason Clark¹  Oleksandr Misiats²  Viktoriia Mogylova³  Oleksandr Stanzhytskyi⁴ 

[1] College of Engineering Oregon State University Corvallis;Department of Mathematics Virginia Commonwealth University Richmond;Department of Physics and Mathematics Igor Sikorsky Kyiv Polytechnic Institute;Department of Mathematics Taras Shevchenko National University of Kyiv

关键词: Stochastic integral;    mild solution;    semigroup;    white noise;    delay differential equation;    invariant measure;   

DOI  :  10.58997/ejde.2023.35

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a priory uniform in time bounds for the solutions in the appropriate Hilbert spaces. These bounds enable us to establish the existence of invariant measure based on Krylov-Bogoliubov theorem on the tightness of the family of measures. Finally, under certain assumptions on nonlinearities, we establish the uniqueness of invariant measures.

【 授权许可】

CC BY