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Measure attractors and random attractors for stochastic partial differential equations 

Author: B. Schmalfuβ a
Affiliation:   a Fachbereich Angewandte Naturwissenschaften, FH Merseburg, Merseburg, Germany
DOI: 10.1080/07362999908809649
Publication Frequency: 6 issues per year
Published in: journal Stochastic Analysis and Applications, Volume 17, Issue 6 1999 , pages 1075 - 1101
Formats available: PDF (English)
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Abstract

In the theory of stochastic differential equations we can distinguish between two kinds of attractors. The first one is the attractor (measure attractor) with respect to the Markov semigroup generated by a stochastic differential equation. The second meaning of attractors (random attractors) is to be understood with respect to each trajectory of the random equation. The aim of this paper is to bring together the two meanings of attractors. In particular, we show the existence of measure attractors if random attractors exist. We can also show the uniqueness of the stationary distributions of the stochastic Navier-Stokes equation if the viscosity is large
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