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Probability density for a hyperbolic SPDEwith 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 solutionof a hyperbolic SPDE with free term coefficients depending ontime, under hypoelliptic non degeneracy conditions. The resultextends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensionalsetting.

Keywords

Malliavin calculus. Stochastic partial differentialequations. Two-parameter processes.

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References

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