Convergence in Dirichlet law of certain stochastic integrals.

Chorro, Christophe

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We consider the random vector $u (t, \underset{̲}{x}) = (u (t, x_{1}), \dots, u (t, x_{d}))$ , where $t > 0, x_{1}, \dots, x_{d}$ are distinct points of $ℝ^{2}$ 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 $u (t, \underset{̲}{x})$ . 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...