Tail asymptotics for the maximum of perturbed random walk
| dc.creator | Araman, Victor F. | |
| dc.creator | Glynn, Peter W. | |
| dc.date | 2006-10-09 | |
| dc.date.accessioned | 2026-07-07T07:28:51Z | |
| dc.date.available | 2026-07-07T07:28:51Z | |
| dc.description | Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(ξ_n:n\geq 0)$ to produce the process $(S_n+ξ_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum $M_{\infty}=\max \{S_k+ξ_k:k\geq0\}$ 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 $\mathbb{P}(M_{\infty}>x)$ as $x\to\infty$. The tail asymptotics depend greatly on whether the $ξ_n$'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. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051606000000268 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0610271 | |
| dc.identifier | http://arxiv.org/abs/math/0610271 | |
| dc.identifier | Annals of Applied Probability 2006, Vol. 16, No. 3, 1411-1431 | |
| dc.identifier | doi:10.1214/105051606000000268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117887 | |
| dc.subject | Probability | |
| dc.subject | 60K25, 60F17, 68M20, 90F35 (Primary) | |
| dc.title | Tail asymptotics for the maximum of perturbed random walk | |
| dc.type | text |