Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three

Studies the sample path regularity of the solution of a stochastic wave equation in spatial dimension 3. This title proves that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. For spatial covariances given by Riesz kernels, it shows that the Holder exponents are optimal.