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January 2007 Extremal behavior of stochastic integrals driven by regularly varying Lévy processes
Henrik Hult, Filip Lindskog
Ann. Probab. 35(1): 309-339 (January 2007). DOI: 10.1214/009117906000000548

Abstract

We study the extremal behavior of a stochastic integral driven by a multivariate Lévy process that is regularly varying with index α>0. For predictable integrands with a finite (α+δ)-moment, for some δ>0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Lévy process and we determine its limit measure associated with regular variation on the space of càdlàg functions.

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Henrik Hult. Filip Lindskog. "Extremal behavior of stochastic integrals driven by regularly varying Lévy processes." Ann. Probab. 35 (1) 309 - 339, January 2007. https://doi.org/10.1214/009117906000000548

Information

Published: January 2007
First available in Project Euclid: 19 March 2007

zbMATH: 1121.60029
MathSciNet: MR2303951
Digital Object Identifier: 10.1214/009117906000000548

Subjects:
Primary: 60F17 , 60G17
Secondary: 60G70 , 60H05

Keywords: Extreme values , Lévy processes , regular variation , stochastic integrals

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 1 • January 2007
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