We establish results, concerning existence, uniqueness, and continuous dependence on an initial datum of a mild solution for neutral stochastic integro-differential equations with variable time delay of reaction-diffusion type. We also establish the Markovian property of this solution. Herewith our emphasis is on unbounded domain {x ∈ R d }.

<p style='text-indent:20px;'>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.</p>

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.