Extremal behavior of stochastic integrals driven by regularly varying Lévy processes

Details Extremal behavior of stochastic integrals driven by regularly varying Lévy processes Extremal behavior of stochastic integrals driven by regularly varying Lévy processes

2007-03-27

arxiv.org/abs/math/0703802v1

Annals of Probability 2007, Vol. 35, No. 1, 309-339

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000548 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000548

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.

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