Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces
Analysis of PDEs
2020-11-16 v1 Probability
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.
Keywords
Cite
@article{arxiv.2011.07034,
title = {Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces},
author = {Oleksandr Misiats and Viktoriia Mogylova and Oleksandr Stanzhytskyi},
journal= {arXiv preprint arXiv:2011.07034},
year = {2020}
}