Large deviations from a stationary measure for a class of dissipative PDE's with random kicks

Vojkan Jaksic (1) , Vahagn Nersesyan (2) , Claude-Alain Pillet (3, 4, 5) , Armen Shirikyan (6)

1 Department of Mathematics and Statistics [Montréal]
2 LMV - Laboratoire de Mathématiques de Versailles
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 7332
5 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
6 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We study a class of dissipative PDE’s perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviation principle for occupation measures of the Markov process in question. The proof is based on Kifer’s large deviation criterion, a coupling argument for Markov processes, and an abstract result on large- time asymptotic for generalised Markov semigroups.

Mots clés: dissipative PDE’s; Navier–Stokes system; Ginzburg–Landau equation; large deviations; occupation measures

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Probabilités [math.PR]

Vojkan Jaksic, Vahagn Nersesyan, Claude-Alain Pillet, Armen Shirikyan. Large deviations from a stationary measure for a class of dissipative PDE's with random kicks. Communications on Pure and Applied Mathematics, 2015, 68 (12), pp.2108-2143. ⟨10.1002/cpa.21568⟩. ⟨hal-00760418v2⟩