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1998

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/16907

Taylor expansion of the density in a stochastic heat equation

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Abstract

We prove a general result on asymptotic expansions of densities for families of perturbed Wiener functionals. As an application, we consider a stochastic heat equation driven by a space-time white noise εW˙ t,x, ε ∈ (0, 1]. The main theorem describes the asymptotics, as ε ↓ 0, of the density pε t,x(y) of the solution at a fixed point (t, x) for some particular value y ∈ R, which, in the diffusion case, plays the role of the diagonal.

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Equacions integrals estocàstiques, Càlcul de Malliavin

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Stochastic differential equations, Malliavin calculus

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Articles publicats en revistes (Matemàtiques i Informàtica)

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MÁRQUEZ, David (Márquez Carreras) and SANZ-SOLÉ, Marta. Taylor expansion of the density in a stochastic heat equation. Collectanea Mathematica. 1998. Vol. 49, num. 2-3, pags. 399-415. ISSN 0610-0757. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/16907

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