We expand a multiple symmetric $\alpha$-stable integral $\int \cdots \int f(t_1, \ldots, t_n) dM(t_1) \ldots dM(t_n)$ into a LePage type multiple series of transformed arrival times of a Poisson process. An exact evaluation of the limit of appropriately normalized tail distribution results from this representation.
Publié le : 1989-10-14
Classification:
Multiple stochastic integral,
stable Levy process,
Poisson process,
60G57,
60E07,
60H05
@article{1176991170,
author = {Samorodnitsky, Gennady and Szulga, Jerzy},
title = {An Asymptotic Evaluation of the Tail of a Multiple Symmetric $\alpha$- Stable Integral},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1503-1520},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991170}
}
Samorodnitsky, Gennady; Szulga, Jerzy. An Asymptotic Evaluation of the Tail of a Multiple Symmetric $\alpha$- Stable Integral. Ann. Probab., Tome 17 (1989) no. 4, pp. 1503-1520. http://gdmltest.u-ga.fr/item/1176991170/