On exponential convergence to a stationary measure for a class of random dynamical systems
Journées équations aux dérivées partielles (2001), article no. 9, 10 p.

For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

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     author = {Sergei B. Kuksin},
     title = {On exponential convergence to a stationary measure for a class of random dynamical systems},
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     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.593},
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Sergei B. Kuksin. On exponential convergence to a stationary measure for a class of random dynamical systems. Journées équations aux dérivées partielles (2001), article  no. 9, 10 p. doi : 10.5802/jedp.593. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.593/

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[KA] L. Kantorovich, G. Akilov Functional analysis (in sbauRussian). Moscow, Nauka, 1977. | MR | Zbl

[KS1] S. Kuksin, A. Shirikyan, Stochastic dissipative PDEs and Gibbs measure, Commun. Math. Phys. 213 (2000), 291-330. | MR | Zbl

[KS2] S. Kuksin, A. Shirikyan A coupling approach to randomly forced nonlinear PDEs 1, to appear in Commun. Math. Phys. | MR | Zbl

[KPS] S. Kuksin, A. Piatnitskii, A. Shirikyan, A coupling approach to randomly forced nonlinear PDEs. 2, preprint (April, 2001). | MR

[Lin] T. Lindvall, Lectures on the Coupling Methods, New York, John Willey & Sons, 1992. | MR | Zbl

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