Geodesic
Probability Theory
Large deviations for invariant measures of general stochastic reaction–diffusion systems
[Grandes déviations pour les mesures invariantes de systèmes généraux d'équations de réaction–diffusion stochastiques]

Présenté par : Paul Malliavin

Cerrai, Sandra1 ; Röckner, Michael2
1 Dip. di Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
2 Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Comptes Rendus. Mathématique, Tome 337 (2003) no. 9, pp. 597-602.

Voir la notice de l'article provenant de la source Numdam

In this paper we prove a large deviations principle for the invariant measures of a class of reaction–diffusion systems in bounded domains of ℝ d ,d⩾1, perturbed by a noise of multiplicative type. We consider reaction terms which are not Lipschitz-continuous and diffusion coefficients in front of the noise which are not bounded and may be degenerate.

Dans cet article on prouve un principe de grandes déviations pour les mesures invariantes de systèmes de réaction–diffusion stochastiques dans des domaines bornés de ℝ d ,d⩾1, perturbés par un bruit multiplicatif. On considère des termes de réaction qui ne sont pas Lipschitz-continus et des coefficients de diffusion qui ne sont pas bornés et peuvent être dégénérés.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.09.015

Cerrai, Sandra 1 ; Röckner, Michael 2

1 Dip. di Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
2 Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany 
@article{CRMATH_2003__337_9_597_0,
     author = {Cerrai, Sandra and R\"ockner, Michael},
     title = {Large deviations for invariant measures of general stochastic reaction{\textendash}diffusion systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {597--602},
     publisher = {Elsevier},
     volume = {337},
     number = {9},
     year = {2003},
     doi = {10.1016/j.crma.2003.09.015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2003.09.015/}
}
TY  - JOUR
AU  - Cerrai, Sandra
AU  - Röckner, Michael
TI  - Large deviations for invariant measures of general stochastic reaction–diffusion systems
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 597
EP  - 602
VL  - 337
IS  - 9
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2003.09.015/
DO  - 10.1016/j.crma.2003.09.015
LA  - en
ID  - CRMATH_2003__337_9_597_0
ER  - 
%0 Journal Article
%A Cerrai, Sandra
%A Röckner, Michael
%T Large deviations for invariant measures of general stochastic reaction–diffusion systems
%J Comptes Rendus. Mathématique
%D 2003
%P 597-602
%V 337
%N 9
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2003.09.015/
%R 10.1016/j.crma.2003.09.015
%G en
%F CRMATH_2003__337_9_597_0
Cerrai, Sandra; Röckner, Michael. Large deviations for invariant measures of general stochastic reaction–diffusion systems. Comptes Rendus. Mathématique, Tome 337 (2003) no. 9, pp. 597-602. doi : 10.1016/j.crma.2003.09.015. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2003.09.015/

[1] Azencott, R. Grandes déviations et applications, École d'Été de Probabilités de Saint-Flour VII, Lecture Notes in Math., 774, Springer-Verlag, 1980

[2] Cerrai, S. Second Order PDE's in Finite and Infinite Dimension. A Probabilistic Approach, Lecture Notes in Math., 1762, Springer-Verlag, 2001

[3] Cerrai, S. Stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term, Probab. Theory Related Fields, Volume 125 (2003), pp. 271-304

[4] S. Cerrai, M. Röckner, Large deviations for stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term, Ann. Probab., in press

[5] Freidlin, M.I. Random perturbations of reaction–diffusion equations: the quasi deterministic approximation, Trans. Amer. Math. Soc., Volume 305 (1988), pp. 665-697

[6] Sowers, R. Large deviations for a reaction–diffusion equation with non-Gaussian perturbation, Ann. Probab., Volume 20 (1992), pp. 504-537

[7] Sowers, R. Large deviations for the invariant measure of a reaction–diffusion equation with non-Gaussian perturbations, Probab. Theory Related Fields, Volume 92 (1992), pp. 393-421

Cité par Sources :