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Probability density for a hyperbolic SPDE with time dependent coefficients

Published online by Cambridge University Press:  17 August 2007

Marta Sanz-Solé  and
Iván Torrecilla-Tarantino
Marta Sanz-Solé
Affiliation:
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; marta.sanz@ub.edu; itorrecilla@ub.edu
Iván Torrecilla-Tarantino
Affiliation:
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; marta.sanz@ub.edu; itorrecilla@ub.edu
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Abstract

We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional setting.

Keywords

Malliavin calculus. Stochastic partial differential equations. Two-parameter processes.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 365 - 380
Copyright
© EDP Sciences, SMAI, 2007

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References

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