Continuity of symmetric stable processes
The sample path continuity of real, symmetric separable in probability p- stable processes, \(0<p<2\), on a compact metric of a pseudometric space (T,\(\tau)\) is analysed. For \(0<p<1\) necessary and sufficient conditions are obtained for a.s. path continuity, for unboundedness and for a.s. discontinuity together with boundedness in terms of stochastic integral representations of the process. In case \(1\leq p<2\) sufficient conditions for a.s. path continuity are given and some conjectures on the stable version of the Dudley-Fernique theorem are presented. In the case of continuous version of stochastic spectral representation for any p-stable process a.s. continuity at each point of T is equivalent to a.s. path continuity.
stable version of the Dudley-Fernique theorem
scientific article; zbMATH DE number 4105967