Expansion of the density: a Wiener-chaos approach

We prove a Taylor expansion of the density pε(y) of a Wiener functional Fε with Wiener-chaos decomposition Fε=y+∑∞n=1εnIn(fn), ε∈(0,1]. Using Malliavin calculus, a precise description of the coefficients in the development in terms of the multiple integrals In(fn) is provided. This general result is...

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Detalles Bibliográficos
Autores: Márquez, David (Márquez Carreras), Sanz-Solé, Marta
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1999
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/23364
Acceso en línea:https://hdl.handle.net/2445/23364
Access Level:acceso abierto
Palabra clave:Equacions diferencials estocàstiques
Càlcul de Malliavin
Probabilitats
Malliavin calculus
Probabilities
Stochastic differential equations
Descripción
Sumario:We prove a Taylor expansion of the density pε(y) of a Wiener functional Fε with Wiener-chaos decomposition Fε=y+∑∞n=1εnIn(fn), ε∈(0,1]. Using Malliavin calculus, a precise description of the coefficients in the development in terms of the multiple integrals In(fn) is provided. This general result is applied to the study of the density in two examples of hyperbolic stochastic partial differential equations with linear coefficients, where the driving noise has been perturbed by a coefficient ε.