Large deviations for stochastic PDE with Lévy noise |
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Authors: | Andrzej ?wi?ch Jerzy Zabczyk |
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Affiliation: | a School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA b Institute of Mathematics, Polish Academy of Sciences, ?niadeckich 8, 00-950 Warsaw, Poland |
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Abstract: | 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. |
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Keywords: | Large deviation principle Lé vy process Viscosity solutions Integro-PDE Hamilton-Jacobi-Bellman equation Stochastic PDE |
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