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1999

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/23364

Expansion of the density: a Wiener-chaos approach

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https://projecteuclid.org/euclid.bj/1173147906

Abstract

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.

Subject

Equacions diferencials estocàstiques, Càlcul de Malliavin, Probabilitats

Subject (English)

Malliavin calculus, Probabilities, Stochastic differential equations

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MÁRQUEZ, David (Márquez Carreras) and SANZ-SOLÉ, Marta. Expansion of the density: a Wiener-chaos approach. Bernoulli. 1999. Vol. 5, num. 2, pags. 257-274. ISSN 1350-7265. [consulted: 12 of June of 2026]. Available at: https://hdl.handle.net/2445/23364

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