Expansion of the density: A Wiener-chaos approach
type: Item
instance of: scholarly article
title: Expansion of the density: A Wiener-chaos approach
zbMATH Open document ID: 0924.60030
DOI: 10.2307/3318435
author: David Márquez-Carreras
author: Marta Sanz-Solé
published in: Bernoulli
publication date: 1999-11-08T00:00:00Z
full work available at URL: http://hdl.handle.net/2445/23364
review text: A Wiener functional with Wiener chaos decomposition \(F^\varepsilon=y+\sum_{n=1}^\infty\varepsilon^nI_n(f_n)\) depends on a small parameter \(\varepsilon\). Assuming that the variable \(F=F^1\) belongs to appropriate Sobolev spaces, it is proved that \(F^\varepsilon\) is smooth with respect to \(\varepsilon\). Then, under a nondegeneracy condition on the Malliavin matrix of \(F^\varepsilon\), an expansion for the density \(p^\varepsilon\) taken at the mean value \(y\) is obtained. Finally, this result is applied to two classes of hyperbolic stochastic partial differential equations with small noise.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 1294460
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: probability densities
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: Wiener functionals
reviewed by: Jean Picard
MaRDI profile type: Publication
OpenAlex ID: W2015005761
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description: scientific article; zbMATH DE number 1294460