Asymptotic behavior of stochastic functional differential evolution equation
DOI:
https://doi.org/10.58997/ejde.2023.35Keywords:
Stochastic integral, mild solution, semigroup, white noise, delay differential equation, invariant measureAbstract
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.
For more information see https://ejde.math.txstate.edu/Volumes/2023/35/abstr.html
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Copyright (c) 2023 Jason Clark, Oleksandr Misiats, Viktoriia Mogylova, Oleksandr Stanzhytskyi
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