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

Sergei B. Kuksin

Journées équations aux dérivées partielles (2001)

  • page 1-10
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Kuksin, 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

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

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