Mersenne banner

Books, Proceedings and Seminars of Centre Mersenne

  • Books
  • Seminars
  • Conferences
  • All
  • Author
  • Title
  • References
  • Full text
NOT
Between and
  • All
  • Author
  • Title
  • Date
  • References
  • Keywords
  • Full text
  • Previous
  • Journées équations aux dérivées partielles
  • Year 2001
  • article no. 9
  • Next
On exponential convergence to a stationary measure for a class of random dynamical systems
Sergei B. Kuksin
Journées équations aux dérivées partielles (2001), article no. 9, 10 p.
  • 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.

  • Article information
  • Export
  • How to cite
MR   Zbl
DOI: 10.5802/jedp.593
  • BibTeX
  • RIS
  • EndNote
@incollection{JEDP_2001____A9_0,
     author = {Sergei B. Kuksin},
     title = {On exponential convergence to a stationary measure for a class of random dynamical systems},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {9},
     pages = {1--10},
     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.593},
     zbl = {01808685},
     mrnumber = {1843410},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.593/}
}
TY  - JOUR
AU  - Sergei B. Kuksin
TI  - On exponential convergence to a stationary measure for a class of random dynamical systems
JO  - Journées équations aux dérivées partielles
PY  - 2001
SP  - 1
EP  - 10
PB  - Université de Nantes
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.593/
DO  - 10.5802/jedp.593
LA  - en
ID  - JEDP_2001____A9_0
ER  - 
%0 Journal Article
%A Sergei B. Kuksin
%T On exponential convergence to a stationary measure for a class of random dynamical systems
%J Journées équations aux dérivées partielles
%D 2001
%P 1-10
%I Université de Nantes
%U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.593/
%R 10.5802/jedp.593
%G en
%F JEDP_2001____A9_0
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/
  • References
  • Cited by

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

[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

Cited by Sources:

Web publisher : Published by : Developed by :
  • Follow us