Extremal Behavior of Stochastic Integrals Driven by Regularly Varying Lévy Processes

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 jum...

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Veröffentlicht in:	The Annals of probability 2007-01, Vol.35 (1), p.309-339
Hauptverfasser:	Hult, Henrik, Lindskog, Filip
Format:	Artikel
Sprache:	eng
Schlagworte:	60F17 60G17 60G70 60H05 Borel sets Distribution theory Exact sciences and technology extreme values General topics Levy processes limit-theorems Lévy processes Markov processes Mathematical functions Mathematical integrals Mathematical models Mathematical theorems Mathematical vectors Mathematics Probability Probability and statistics Probability theory and stochastic processes Random variables Regular variation Sciences and techniques of general use Separable spaces Statistics Step functions Stochastic analysis stochastic integrals Stochastic processes Studies
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Beschreibung
Zusammenfassung:	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.
ISSN:	0091-1798 2168-894X 2168-894X
DOI:	10.1214/009117906000000548