Necessary and sufficient conditions are presented for the measurability of $p$th order or symmetric stable stochastic processes and for the integrability or absolute continuity of sample paths of symmetric stable processes. Also obtained are sufficient conditions for absolute continuity of $p$th order processes.
"Some Path Properties of $p$th Order and Symmetric Stable Processes." Ann. Probab. 8 (6) 1148 - 1156, December, 1980. https://doi.org/10.1214/aop/1176994575