Level crossings of absolutely continuous stationary symmetric .-stable processes

Authors
Adler Robert, Samorodnitsky, Gennady
Citation
Adler Robert, et Samorodnitsky, Gennady, Level crossings of absolutely continuous stationary symmetric .-stable processes, Annals of applied probability , 7(2), 1997, pp. 460-493
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
7
Issue
2
Year of publication
1997
Pages
460 - 493
Database
ACNP
SICI code
Abstract
We describe the mean rate at which a general absolutely continuous stationary S.S process crosses a high level. Only nondegeneracy assumptions are imposed in the case 1<.<2. The same results hold for 0<..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.