Sharp Large Deviation Estimates for the Stochastic Heat Equation |
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Authors: | Rovira Carles Tindel Samy |
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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 |
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Abstract: | We consider the family {X, 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is tX=X+b({X})+({X}). Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X}A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes. |
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Keywords: | parabolic SPDE large deviations stochastic Taylor's expansion |
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