We consider the random vector
$u(t,\underline
x)=(u(t,x_1),\dots,u(t,x_d))$
, where t > 0, x1,...,xd
are
distinct points of
$\mathbb{R}^2$
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
[10], sufficient conditions are given ensuring existence and
smoothness of
density for
$u(t,\underline x)$
. We study here the positivity of such
density. Using
techniques developped in [1] (see also [9]) based
on Analysis on an
abstract Wiener space, we characterize the set of points
$y\in\mathbb{R}^d$
where the density is
positive and we prove that, under suitable assumptions, this set is
$\mathbb{R}^d$
.