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On dissipative systems perturbed by bounded random kick-forces

Published online by Cambridge University Press:  30 September 2002

SERGEI KUKSIN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK and Steklov Institute of Mathematics, 8 Gubkina Street, 117966 Moscow, Russia (e-mail: S.B.Kuksin@ma.hw.ac.uk)
ARMEN SHIRIKYAN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK and Institute of Mechanics of MSU, 1 Michurinskii Avenue, 119899 Moscow, Russia (e-mail: A.Shirikyan@ma.hw.ac.uk)

Abstract

In this paper, we continue our investigation of dissipative PDE's forced by random bounded kick-forces and of the corresponding random dynamical system (RDS) in function spaces. It has been proved that the domain \mathcal{A} of attainability from zero (which is a compact subset of a function space) is invariant for the RDS associated with the original equation and carries a stationary measure \mu, which is unique among all measures supported by \mathcal{A}. Here we show that \mu is the unique stationary measure for the RDS in the whole space and study its ergodic properties.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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