Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

Abstract

We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'{e}vy process and we determine its limit measure associated with regular variation on the space of c\{a}dl\{a}g functions.Comment: Published at http://dx.doi.org/10.1214/009117906000000548 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Topics: Mathematics - Probability, 60F17, 60G17 (Primary) 60H05, 60G70 (Secondary)
Publisher: 'Institute of Mathematical Statistics'
Year: 2007
DOI identifier: 10.1214/009117906000000548
OAI identifier: oai:arXiv.org:math/0703802

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