Open AccessInvariant measure for neutral stochastic functional differential equations with non-Lipschitz coefficients
Author(s) -
Andriy Stanzhytskyi,
Oleksandr Stanzhytskyi,
Oleksandr Misiats
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2022005
Subject(s) - lipschitz continuity , mathematics , invariant measure , invariant (physics) , nonlinear system , hilbert space , stochastic differential equation , mathematical analysis , differential equation , pure mathematics , measure (data warehouse) , mathematical physics , physics , computer science , ergodic theory , quantum mechanics , database
In this work we study the long time behavior of nonlinear stochastic functional-differential equations of neutral type in Hilbert spaces with non-Lipschitz nonlinearities. We establish the existence of invariant measures in the shift spaces for such equations. Our approach is based on Krylov-Bogoliubov theorem on the tightness of the family of measures.