On exponential convergence to a stationary measure for a class of random dynamical systems
Kuksin, Sergei B.
Journées équations aux dérivées partielles, (2001), p. 1-10 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

@article{JEDP_2001____A9_0,
     author = {Kuksin, Sergei B.},
     title = {On exponential convergence to a stationary measure for a class of random dynamical systems},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2001},
     pages = {1-10},
     doi = {10.5802/jedp.593},
     mrnumber = {1843410},
     zbl = {01808685},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2001____A9_0}
}

Kuksin, Sergei B. On exponential convergence to a stationary measure for a class of random dynamical systems. Journées équations aux dérivées partielles,  (2001), pp. 1-10. doi : 10.5802/jedp.593. http://gdmltest.u-ga.fr/item/JEDP_2001____A9_0/

[Du] R. Dudley Real analysis and probability, Wadsworth&Brooks/Cole, 1989. | MR 982264 | Zbl 0686.60001

[KA] L. Kantorovich, G. Akilov Functional analysis (in sbauRussian). Moscow, Nauka, 1977. | MR 788496 | Zbl 0555.46001

[KS1] S. Kuksin, A. Shirikyan, Stochastic dissipative PDEs and Gibbs measure, Commun. Math. Phys. 213 (2000), 291-330. | MR 1785459 | Zbl 0974.60046

[KS2] S. Kuksin, A. Shirikyan A coupling approach to randomly forced nonlinear PDEs 1, to appear in Commun. Math. Phys. | MR 1845328 | Zbl 0991.60056

[KPS] S. Kuksin, A. Piatnitskii, A. Shirikyan, A coupling approach to randomly forced nonlinear PDEs. 2, preprint (April, 2001). | MR 1927233

[Lin] T. Lindvall, Lectures on the Coupling Methods, New York, John Willey & Sons, 1992. | MR 1180522 | Zbl 0850.60019