Asymptotic behavior of stochastic functional differential evolution equation

Date

2023-04-12

Authors

Clark, Jason
Misiats, Oleksandr
Mogylova, Viktoriia
Stanzhytskyi, Oleksandr

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

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.

Description

Keywords

Stochastic integral, Mild solution, Semigroup, White noise, Delay differential equation, Invariant measure

Citation

Clark, J., Misiats, O., Mogylova, V., & Stanzhytskyi, O. (2023). Asymptotic behavior of stochastic functional differential evolution equation. <i>Electronic Journal of Differential Equations, 2023</i>(35), pp. 1-21.

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Attribution 4.0 International

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