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april 1999 Expansion of the density: a Wiener-chaos approach
David Márquez-Carreras, Marta Sanz-Solé
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Bernoulli 5(2): 257-274 (april 1999).

Abstract

We prove a Taylor expansion of the density p ε (y) of a Wiener functional F ε with Wiener-chaos decomposition F ε =y+ n =1 ε n nI(f n) , ε (0,1] . Using Malliavin calculus, a precise description of the coefficients in the development in terms of the multiple integrals I n (f n) 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 .

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David Márquez-Carreras. Marta Sanz-Solé. "Expansion of the density: a Wiener-chaos approach." Bernoulli 5 (2) 257 - 274, april 1999.

Information

Published: april 1999
First available in Project Euclid: 5 March 2007

zbMATH: 0924.60030
MathSciNet: MR1681698

Keywords: Malliavin calculus , probability densities , Stochastic partial differential equations , Wiener functionals

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 2 • april 1999
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