Approximation and support theorem for a two space-dimensional wave equation

Annie Millet; Marta Sanz-Solé

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arXiv · math/9804148

Approximation and support theorem for a two space-dimensional wave equation

Annie Millet·Marta Sanz-Solé

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Abstract

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, aproximation in the $L^p$ norm, for $p\geq 1$ is also proved.

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Annie Millet, Marta Sanz-Solé. 1998-04-03. Approximation and support theorem for a two space-dimensional wave equation. https://arxiv.org/abs/math/9804148

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