By Robert C. Dalang
The authors of this identify learn the pattern direction regularity of the answer of a stochastic wave equation in spatial measurement d three. The using noise is white in time and with a spatially homogeneous covariance outlined as a made from a Riesz kernel and a tender functionality. The authors end up that at any mounted time, a.s., the pattern paths within the spatial variable belong to convinced fractional Sobolev areas. additional, the authors receive joint Holder continuity within the time and area variables. Their effects depend on an in depth research of homes of the stochastic necessary utilized in the rigorous formula of the s.p.d.e., as brought by means of Dalang and Mueller (2003). Sharp effects on one- and two-dimensional house and time increments of generalized Riesz potentials are a vital factor within the research of the matter. For spatial covariances given by means of Riesz kernels, the authors express that the Holder exponents that they receive are optimum.
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