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.