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May 1997 Level crossings of absolutely continuous stationary symmetric $\alpha$-stable processes
Robert Adler, Gennady Samorodnitsky
Ann. Appl. Probab. 7(2): 460-493 (May 1997). DOI: 10.1214/aoap/1034625340

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.

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Robert Adler. Gennady Samorodnitsky. "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

Information

Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0883.60026
MathSciNet: MR1442322
Digital Object Identifier: 10.1214/aoap/1034625340

Subjects:
Primary: 60G10 , 60G70
Secondary: 60G17 , 60G18

Keywords: level crossings , Stable processes

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 2 • May 1997
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