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

Authors :
Armen Shirikyan
Claude-Alain Pillet
Vahagn Nersesyan
Vojkan Jaksic
Department of Mathematics and Statistics [Montréal]
McGill University = Université McGill [Montréal, Canada]
Laboratoire de Mathématiques de Versailles (LMV)
Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
CPT - E5 Physique statistique et systèmes complexes
Centre de Physique Théorique - UMR 7332 (CPT)
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Fédération de Recherche des Unités de MAthématiques de Marseille (FRUMAM)
Avignon Université (AU)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Analyse, Géométrie et Modélisation (AGM - UMR 8088)
Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
ANR-11-BS01-0017,EMAQS,Estimation et manipulation à l'échelle Quantique(2011)
ANR-11-BS01-0015,STOSYMAP,Systèmes stochastiques en mathématiques et physique mathématique(2011)
ANR-11-IDEX-0001,Amidex,INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE(2011)
ANR-11-LABX-0023,MME-DII,Modèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions(2011)
Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Avignon Université (AU)-Université de Toulon (UTLN)
Source :
Communications on Pure and Applied Mathematics, Communications on Pure and Applied Mathematics, 2015, 68 (12), pp.2108-2143. ⟨10.1002/cpa.21568⟩, Communications on Pure and Applied Mathematics, Wiley, 2015, 68 (12), pp.2108-2143. ⟨10.1002/cpa.21568⟩
Publication Year :
2015
Publisher :
Wiley, 2015.

Abstract

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 Lyapunov-Schmidt type reduction, and an abstract result on large-time asymptotic for generalised Markov semigroups.<br />Comment: 42 pages

Subjects

Subjects :
General Mathematics
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Physical sciences
Markov process
Measure (mathematics)
large deviations
symbols.namesake
Mathematics - Analysis of PDEs
35Q30, 76D05, 60B12, 60F10
Integer
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Applied mathematics
Navier–Stokes system
Mathematical Physics
Ginzburg–Landau equation
Mathematics
Markov chain
Applied Mathematics
Probability (math.PR)
Mathematical analysis
Mathematical Physics (math-ph)
Coupling (probability)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Bounded function
dissipative PDE’s
occupation measures
symbols
Dissipative system
Large deviations theory
Mathematics - Probability
Analysis of PDEs (math.AP)

Details

ISSN :
00103640 and 10970312
Volume :
68
Database :
OpenAIRE
Journal :
Communications on Pure and Applied Mathematics
Accession number :
edsair.doi.dedup.....d166f0900424c19a9754d430d96daa03
Full Text :
https://doi.org/10.1002/cpa.21568
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