Level crossings of absolutely continuous stationary symmetric $\alpha$-stable processes

Abstract

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.