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July 1999 Asymptotic Behavior of Conditional Laws and Moments of $\infty$-Stable Random Vectors, with Application to Upcrossing Intensities
J. M. P. Albin, M. R. Leadbetter
Ann. Probab. 27(3): 1468-1500 (July 1999). DOI: 10.1214/aop/1022677455

Abstract

We derive upper bounds for the conditional moment $\mathbf{E} \{| X|^{\varrho}|Y=y\}$ of a strictly $\alpha$-stable random vector (X,Y) when $\alpha\neq 1$ and $\varrho\leq 2$ and prove weak convergences for the conditional law $(X/u|Y= u)$ as $u \to \infty$ when $\alpha > 1$. As an example of application, we derive a new result in crossing theory for $\alpha$-stable processes.

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J. M. P. Albin. M. R. Leadbetter. "Asymptotic Behavior of Conditional Laws and Moments of $\infty$-Stable Random Vectors, with Application to Upcrossing Intensities." Ann. Probab. 27 (3) 1468 - 1500, July 1999. https://doi.org/10.1214/aop/1022677455

Information

Published: July 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0963.60006
MathSciNet: MR1733156
Digital Object Identifier: 10.1214/aop/1022677455

Subjects:
Primary: 60E07, 60F99, 62E20
Secondary: 60G70, 60G99

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 3 • July 1999
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