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

Jakšić Vojkan | Zendy; Nersesyan Vahagn | Zendy; Pillet ClaudeAlain | Zendy; Shirikyan Armen | Zendy

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

Author(s) -

Jakšić Vojkan,

Nersesyan Vahagn,

Pillet ClaudeAlain,

Shirikyan Armen

Publication year - 2015

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21568

Subject(s) - measure (data warehouse) , dissipative system , mathematics , markov chain , markov process , bounded function , class (philosophy) , statistical physics , markov property , large deviations theory , markov model , mathematical analysis , computer science , statistics , physics , quantum mechanics , database , artificial intelligence

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.

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