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arXiv · 2011.07034

Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces

Oleksandr Misiats·Viktoriia Mogylova·Oleksandr Stanzhytskyi
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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.

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Oleksandr Misiats, Viktoriia Mogylova, Oleksandr Stanzhytskyi. 2020-11-13. Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces. https://arxiv.org/abs/2011.07034

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