학술논문
ASYMPTOTIC BEHAVIOR OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EVOLUTION EQUATION.
Document Type
Article
Source
Subject
Language
ISSN
1550-6150
Abstract
In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a priory uniform in time bounds for the solutions in the appropriate Hilbert spaces. These bounds enable us to establish the existence of invariant measure based on Krylov-Bogoliubov theorem on the tightness of the family of measures. Finally, under certain assumptions on nonlinearities, we establish the uniqueness of invariant measures. [ABSTRACT FROM AUTHOR]