Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
Balan, Raluca M. (University of Ottawa. Department of Mathematics and Statistics (Canada))
Quer i Sardanyons, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Song, Jian (Shandong University. School of Mathematics (China))

Date:	2019
Abstract:	In this article, we consider the stochastic wave equation on R × R, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions γ (in time) and f (in space), which are the Fourier transforms of tempered measures ν on R, respectively µ on R. Our main result shows that the law of the solution u(t, x) of this equation is absolutely continuous with respect to the Lebesgue measure.
Grants:	Ministerio de Economía y Competitividad MTM2015-67802-P
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Gaussian noise ; Stochastic partial differential equations ; Malliavin calculus
Published in:	Electronic Journal of Probability, Vol. 24, Issue 106 (2019) , p. 1-43, ISSN 1083-6489

DOI: 10.1214/19-EJP363

44 p, 619.5 KB

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