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Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks
Authors:Vojkan Jakšić  Vahagn Nersesyan  Claude‐Alain Pillet  Armen Shirikyan
Affiliation:1. Department of Mathematics and Statistics, McGill University, Montreal, Canada;2. Laboratoire de Mathématiques UMR CNRS 8100, Université de Versailles‐Saint‐Quentinen‐Yvelines, Versailles, France;3. Aix Marseille Université CNRS, CPT, UMR 7332, Marseille, France;4. Université de Toulon CNRS, CPT, UMR 7332, La Garde, France;5. Department of Mathematics, University of Cergy‐Pontoise CNRS UMR 8088, Cergy‐Pontoise, France
Abstract:We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, 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 deviations 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 generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.
Keywords:
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