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Invariant Measure for Neutral Stochastic Functional Differential Equations with Non-Lipschitz Coefficients
Andriy Stanzhytskyi, Oleksandr Stanzhytskyi, Oleksandr Misiats · 2021-11-12 · via math.PR updates on arXiv.org

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.

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