Large deviations for stochastic PDE with Lévy noise

We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Lévy noise. We use general large deviations theorems of Varadhan and Bryc coupled with the techniques of Feng and Kurtz (2006) [15], viscosity solutions of integro-partial differen...

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Bibliographic Details
Published in:Journal of functional analysis 2011-02, Vol.260 (3), p.674-723
Main Authors: Święch, Andrzej, Zabczyk, Jerzy
Format: Article
Language:English
Subjects:
Hamilton–Jacobi–Bellman equation
Integro-PDE
Large deviation principle
Lévy process
Stochastic PDE
Viscosity solutions
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Summary:We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Lévy noise. We use general large deviations theorems of Varadhan and Bryc coupled with the techniques of Feng and Kurtz (2006) [15], viscosity solutions of integro-partial differential equations in Hilbert spaces, and deterministic optimal control methods. The Laplace limit is identified as a viscosity solution of a Hamilton–Jacobi–Bellman equation of an associated control problem. We also establish exponential moment estimates for solutions of stochastic evolution equations driven by Lévy noise. General results are applied to stochastic hyperbolic equations perturbed by subordinated Wiener process.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2010.09.016