# On exponential convergence to a stationary measure for a class of random dynamical systems

Journées équations aux dérivées partielles (2001)

- page 1-10
- ISSN: 0752-0360

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topKuksin, Sergei B.. "On exponential convergence to a stationary measure for a class of random dynamical systems." Journées équations aux dérivées partielles (2001): 1-10. <http://eudml.org/doc/93420>.

@article{Kuksin2001,

abstract = {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.},

author = {Kuksin, Sergei B.},

journal = {Journées équations aux dérivées partielles},

language = {eng},

pages = {1-10},

publisher = {Université de Nantes},

title = {On exponential convergence to a stationary measure for a class of random dynamical systems},

url = {http://eudml.org/doc/93420},

year = {2001},

}

TY - JOUR

AU - Kuksin, Sergei B.

TI - On exponential convergence to a stationary measure for a class of random dynamical systems

JO - Journées équations aux dérivées partielles

PY - 2001

PB - Université de Nantes

SP - 1

EP - 10

AB - 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.

LA - eng

UR - http://eudml.org/doc/93420

ER -

## References

top- [Du] R. DudleyReal analysis and probability, Wadsworth&Brooks/Cole, 1989. Zbl0686.60001MR982264
- [KA] L. Kantorovich, G. AkilovFunctional analysis (in sbauRussian). Moscow, Nauka, 1977. Zbl0555.46001MR788496
- [KS1] S. Kuksin, A. Shirikyan, Stochastic dissipative PDEs and Gibbs measure, Commun. Math. Phys. 213 ( 2000), 291-330. Zbl0974.60046MR1785459
- [KS2] S. Kuksin, A. ShirikyanA coupling approach to randomly forced nonlinear PDEs 1, to appear in Commun. Math. Phys. Zbl0991.60056MR1845328
- [KPS] S. Kuksin, A. Piatnitskii, A. Shirikyan, A coupling approach to randomly forced nonlinear PDEs. 2, preprint (April, 2001). MR1927233
- [Lin] T. Lindvall, Lectures on the Coupling Methods, New York, John Willey & Sons, 1992. Zbl0850.60019MR1180522