Invariant measure for neutral stochastic functional differential equations with non-Lipschitz coefficients

Abstract

<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>

On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

“…Regarding stochastic functionaldifferential equations in infinite-dimensional spaces, the monograph [4] is noteworthy. The existence of invariant measures in shift spaces for stochastic functionaldifferential equations with partial derivatives is addressed in works [5][6][7][8]. In this work, the asymptotic behavior of solutions at infinity is investigated using a wellknown method in the theory of differential equations called the method of asymptotic equivalence.…”

Asymptotic behavior of stochastic functional differential evolution equation

“…The results on stochastic functional differential equations include [29,8], which establish the existence of solutions and their stability. Stochastic differential equation of neutral type were studied in [26,16,31]. The work [28] established the comparison principle for such equations.…”

Stabilization of semilinear wave equations with time-dependent variable coefficients and memory

“…The results on stochastic functional differential equations include [29,8], which establish the existence of solutions and their stability. Stochastic differential equation of neutral type were studied in [26,16,31]. The work [28] established the comparison principle for such equations.…”