Volume 7, March 2003
|Page(s)||89 - 114|
|Published online||15 May 2003|
Positivity of the density for the stochastic wave equation in two spatial dimensions
Université Pierre et Marie Curie,
Laboratoire de Probabilités,
175/179 rue du Chevaleret, 75013 Paris, France; and
Université René Descartes, 45 rue des Saints Pères,
75006 Paris, France; email@example.com.
2 Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; firstname.lastname@example.org.
We consider the random vector , where t > 0, x1,...,xd are distinct points of and u denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé , sufficient conditions are given ensuring existence and smoothness of density for . We study here the positivity of such density. Using techniques developped in  (see also ) based on Analysis on an abstract Wiener space, we characterize the set of points where the density is positive and we prove that, under suitable assumptions, this set is .
Mathematics Subject Classification: 60H15 / 60H07
Key words: Stochastic partial differential equations / Malliavin Calculus / wave equation / probability densities.
© EDP Sciences, SMAI, 2003
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