On sample path properties of semistable processes
The authors show that the well-known correspondence principle between Gaussian and stable processes and measures on \(L_ p\) spaces extends to Banach valued r-semistable index \(\alpha\) processes and measures on \(L_ p\), \(1\leq p<\infty.\) In the second result, it is shown that paths of B-valued r-semistable processes belong to \(L_ p\) with probability zero or one. Finally, several necessary and sufficient conditions for almost sure path absolute continuity for r-semistable B-valued separable processes, under certain conditions on B, are given.
scientific article; zbMATH DE number 4038930
scientific article