Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces

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 approp...

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Published in:arXiv.org 2020-11
Main Authors: Misiats, Oleksandr, Mogylova, Viktoriia, Stanzhytskyi, Oleksandr
Format: Article
Language:English
Subjects:
Differential equations
Existence theorems
Hilbert space
Invariants
Mathematical analysis
Nonlinear equations
Tightness
Uniqueness
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Mogylova, Viktoriia
Stanzhytskyi, Oleksandr
description 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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subjects Differential equations
Existence theorems
Hilbert space
Invariants
Mathematical analysis
Nonlinear equations
Tightness
Uniqueness
title Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces
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