Consider a random walk S=(Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time maximum M∞=max {Sk+ξk:k≥0} of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for ℙ(M∞>x) as x→∞. The tail asymptotics depend greatly on whether the ξn’s are light-tailed or heavy-tailed. In the light-tailed setting, the tail asymptotic is closely related to the Cramér–Lundberg asymptotic for standard random walk.
Publié le : 2006-08-14
Classification:
Perturbed random walk,
Cramér–Lundberg approximation,
tail asymptotics,
coupling,
heavy tails,
60K25,
60F17,
68M20,
90F35
@article{1159804986,
author = {Araman, Victor F. and Glynn, Peter W.},
title = {Tail asymptotics for the maximum of perturbed random walk},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 1411-1431},
language = {en},
url = {http://dml.mathdoc.fr/item/1159804986}
}
Araman, Victor F.; Glynn, Peter W. Tail asymptotics for the maximum of perturbed random walk. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 1411-1431. http://gdmltest.u-ga.fr/item/1159804986/