Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

Vojkan Jakšić,Claude‐Alain Pillet,Armen Shirikyan,Vahagn Nersesyan

doi:10.1002/cpa.21568

Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

Vojkan Jakšić, Claude‐Alain Pillet + Show 2 more

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https://doi.org/10.1002/cpa.21568

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Journal: Communications on Pure and Applied Mathematics	Publication Date: Mar 9, 2015
Citations: 50

Affiliation: McGill University, French National Centre for Scientific Research, Aix-Marseille University, Université de Toulon, Information Processing and System Research Lab, CY Cergy Paris University, Laboratoire de Mathématiques

#Random Force #Unique Stationary Measure + Show 8 more

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Abstract

AbstractWe 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.

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