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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.