We describe the mean rate at which a general absolutely continuous stationary $S \alpha S$ process crosses a high level. Only nondegeneracy assumptions are imposed in the case $1 < \alpha < 2$. The same results hold for $0 < \alpha \leq 1$ under certain conditions, ensuring existence of the required conditional moments and the applicability of the classical integral formula for the expected number of level crossings.
"Level crossings of absolutely continuous stationary symmetric $\alpha$-stable processes." Ann. Appl. Probab. 7 (2) 460 - 493, May 1997. https://doi.org/10.1214/aoap/1034625340