Extremal behavior of stochastic integrals driven by regularly varying Lévy processes

Henrik Hult, Filip Lindskog
2007 Annals of Probability  
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.
doi:10.1214/009117906000000548 fatcat:7iwbytyitvhfpa5zeilznej2mq