ESAIM: P&S, August 2007, Vol. 11, pp. 365-380
DOI: 10.1051/ps:2007024

Probability density for a hyperbolic SPDE with time dependent coefficients

Marta Sanz-Solé and Iván Torrecilla-Tarantino

Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; marta.sanz@ub.edu; itorrecilla@ub.edu

(Received July 10, 2006. Accepted December 26, 2006 Published online 17 August 2007.)

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, PTRF 123 (2002) 453-483 to an infinite dimensional setting.

Mathematics Subject Classification. 60H07, 60H15, 60G60

Key words: Malliavin calculus. Stochastic partial differential equations. Two-parameter processes.


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