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Large Deviations Principle for Stochastic Scalar Conservation Laws

Mariani, Mauro (2010), Large Deviations Principle for Stochastic Scalar Conservation Laws, Probability Theory and Related Fields, 147, 3-4, p. 607-648. http://dx.doi.org/10.1007/s00440-009-0218-6

Type
Article accepté pour publication ou publié
Date
2010
Nom de la revue
Probability Theory and Related Fields
Volume
147
Numéro
3-4
Éditeur
Springer
Pages
607-648
Identifiant publication
Métadonnées
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Auteur(s)
Mariani, Mauro
Résumé (EN)
Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. A second order large deviations principle is therefore investigated, however, this can be only partially proved. The second order rate functional provides a generalization for non-convex fluxes of the functional introduced by Jensen and Varadhan in a stochastic particles system setting.
Mots-clés
Entropy functional; Conservation laws; Large deviations; Stochastic PDE