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Characterization of the support in Hlder norm of a wave equation in dimension three

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Stochastic Partial Differential Equations (SPDEs)

We consider a non-linear stochastic wave equation driven by a Gaussian noise white in time and with a spatial stationary covariance. From results of Dalang and Sanz-Sol (2009), it is known that the sample paths of the random field solution are Hlder continuous, jointly in time and in space. In this lecture, we will establish a characterization of the topological support of the law of the solution to this equation in Hlder norm. This will follow from an approximation theorem, in the convergence of probability, for a sequence of evolution equations driven by a family of regularizations of the driving noise.

This talk is part of the Isaac Newton Institute Seminar Series series.

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