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2001-04

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216655

Asymptotic behaviour of the density in a parabolic SPDE

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Abstract

Consider the density of the solution $X(t, x)$ of a stochastic heat equation with small noise at a fixed $t \in[0, T], x \in[0,1]$. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed.

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Grans desviacions, Càlcul de Malliavin, Equacions diferencials estocàstiques, Equacions diferencials parabòliques

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Large deviations, Malliavin calculus, Stochastic differential equations, Parabolic differential equations

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KOHATSU, Arturo, MÁRQUEZ, David (Márquez Carreras) and SANZ-SOLÉ, Marta. Asymptotic behaviour of the density in a parabolic SPDE. Journal of Theoretical Probability. 2001. Vol. 14, num. 2, pags. 427-462. ISSN 0894-9840. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/216655

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