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

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2021-11-11 DOI:10.3934/eect.2022005

A. Stanzhytskyi, Oleksandr Stanzhytskyi, Oleksandr Misiats

引用次数: 3

Abstract

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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非lipschitz系数中立型随机泛函微分方程的不变测度

本文研究了具有非lipschitz非线性的Hilbert空间中中性型非线性随机泛函微分方程的长时间行为。我们建立了这类方程位移空间中不变测度的存在性。我们的方法是基于测度族紧密性的Krylov-Bogoliubov定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology