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arXiv · 1404.2411

Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case

Francisco J. Delgado-Vences·Marta Sanz-Solé
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Abstract

This paper is a continuation of (Bernoulli 20 (2014) 2169-2216) where we prove a characterization of the support in Hölder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable and null initial conditions. Here, we allow for non-null initial conditions and, therefore, the solution does not possess a stationary property in space. As in (Bernoulli 20 (2014) 2169-2216), the support theorem is a consequence of an approximation result, in the convergence of probability, of a sequence of evolution equations driven by a family of regularizations of the driving noise. However, the method of the proof differs from (Bernoulli 20 (2014) 2169-2216) since arguments based on the stationarity property of the solution cannot be used.

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Francisco J. Delgado-Vences, Marta Sanz-Solé. 2016-03-23. Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case. https://doi.org/10.3150/15-bej704

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