Taylor expansion of the density in a stochastic heat equation

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(...

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Detalles Bibliográficos
Autores: Márquez, David (Márquez Carreras), Sanz-Solé, Marta
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1998
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/16907
Acceso en línea:https://hdl.handle.net/2445/16907
Access Level:acceso abierto
Palabra clave:Equacions integrals estocàstiques
Càlcul de Malliavin
Stochastic differential equations
Malliavin calculus
Descripción
Sumario: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.