Invariant Measure for Neutral Stochastic Functional Differential\n Equations with Non-Lipschitz Coefficients

2021/11/11 by Andriy Stanzhytskyi, Stanzhytskyi, Andriy, Oleksandr Stanzhytskyi +3
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.06492

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we study the long time behavior of nonlinear stochastic\nfunctional-differential equations of neutral type in Hilbert spaces with\nnon-Lipschitz nonlinearities. We establish the existence of invariant measures\nin the shift spaces for such equations. Our approach is based on\nKrylov-Bogoliubov theorem on the tightness of the family of measures.\n

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