Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm

Abstract

A characterization of the support in Hölder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. The result is a consequence of an approximation theorem, in the convergence of probability, for a sequence of evolution equations driven by a family of regularizations of the driving noise.

Published in at http://dx.doi.org/10.3150/13-BEJ554 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Functional Itô calculus and stochastic integral representation of martingales

Cited by in corpus (6)

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• The support of singular stochastic PDEs
• Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case
• Approximation of solutions of the stochastic wave equation by using the Fourier series
• A support theorem for parabolic stochastic PDEs with nondegenerate Hölder diffusion coefficients
• Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise