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

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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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Bernoulli Society for Mathematical Statistics and Probability

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(c) ISI/BS, International Statistical Institute, Bernoulli Society, 2016

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: the non-stationary case