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Abstract: We prove a large deviation principle result for solutions of abstractstochastic evolution equations perturbed by small Levy noise. We use generallarge deviations theorems of Varadhan and Bryc, viscosity solutions ofintegro-partial differential equations in Hilbert spaces, and deterministicoptimal control methods. The Laplace limit is identified as a viscositysolution of a Hamilton-Jacobi-Bellman equation of an associated controlproblem. We also establish exponential moment estimates for solutions ofstochastic evolution equations driven by Levy noise. General results areapplied to stochastic hyperbolic equations perturbed by subordinated Wienerprocess.



Author: Andrzej Swiech, Jerzy Zabczyk

Source: https://arxiv.org/







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