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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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DELGADO VENCES, Francisco javier, SANZ-SOLÉ, Marta. Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: the non-stationary case. _Bernoulli_. 2016. Vol. 22, núm. 3, pàgs. 1572-1597. [consulta: 9 de gener de 2026]. ISSN: 1350-7265. [Disponible a: https://hdl.handle.net/2445/116485]