Clark, JasonMisiats, OleksandrMogylova, ViktoriiaStanzhytskyi, Oleksandr2023-05-232023-05-232023-04-12Clark, 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. 1-21.1072-6691https://hdl.handle.net/10877/16870In 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.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalStochastic integralMild solutionSemigroupWhite noiseDelay differential equationInvariant measureArticle