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Sharp Large Deviation Estimates for the Stochastic Heat Equation
Authors:Rovira  Carles  Tindel  Samy
Affiliation:(1) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;(2) Département de Mathématiques, Institut Galilée - Université Paris 13, Avenue J. B. Clément, 93430 Villetaneuse, France
Abstract:We consider the family {Xepsi, epsige0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is parttXepsi=
$$partial _{x,x}^2 $$
Xepsi+b({Xepsi})+epsisgr({Xepsi})
$$dot W$$
. Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({Xepsi}isinA) as epsisearr0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes.
Keywords:parabolic SPDE  large deviations  stochastic Taylor's expansion
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