Open Access
Translator Disclaimer
april 1999 Expansion of the density: a Wiener-chaos approach
David Márquez-Carreras, Marta Sanz-Solé
Author Affiliations +
Bernoulli 5(2): 257-274 (april 1999).


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 .


Download Citation

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


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


Vol.5 • No. 2 • april 1999
Back to Top