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; firstname.lastname@example.org.
2 Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; email@example.com.
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.