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Invariant measures for dichotomous stochastic differential equations in Hilbert spaces

✍ Scribed by Onno Van Gaans; Sjoerd Verduyn Lunel

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
80 KB
Volume
334
Category
Article
ISSN
1631-073X

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✦ Synopsis

We study existence of invariant measures for semilinear stochastic differential equations in Hilbert spaces. We consider infinite dimensional noise that is white in time and colored in space and we assume that the nonlinearities are Lipschitz continuous. We show that if the equation is 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. To cite this article: O.

πŸ“œ SIMILAR VOLUMES

The Euler scheme for Hilbert space value
The Euler scheme for Hilbert space valued stochastic differential equations
✍ RaΓΊl Fierro; Soledad Torres πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 93 KB

Here we consider stochastic di erential equations whose solutions take values in a Hilbert space. The Euler Scheme for approximating these solutions is used, and the global error is estimated. In addition, solutions are approximated by means of a process which takes values in a ΓΏnite-dimensional sub