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- Title
LONG TERM BEHAVIOR OF DICHOTOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES.
- Authors
Van Gaans, Onno; Verduyn Lunel, Sjoerd
- Abstract
We study existence of invariant measures for semilinear stochastic differential equations in Hilbert spaces. The noise is infinite dimensional, white in time, and colored in space. We show that if the equation is exponentially dichotomous in the sense that the semigroup generated by the linear part is hyperbolic and the Lipschitz constants of the nonlinearities are not too large, then existence of a solution with bounded mean squares implies existence of an invariant measure. Moreover, we show that every bounded solution satisfies a certain "Cauchy condition", which implies that its distributions converge weakly to a limit distribution.
- Subjects
STOCHASTIC differential equations; GRONWALL inequalities; HYPERBOLIC groups; INVARIANT measures; DELAY differential equations; LIPSCHITZ spaces
- Publication
Communications in Contemporary Mathematics, 2004, Vol 6, Issue 3, p349
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199704001379