TY - JOUR

T1 - On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions

AU - Zachary, S.

AU - Foss, S. G.

PY - 2006/11

Y1 - 2006/11

N2 - We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some ? > 0 to a subclass of the class S ? (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the "spatially local" asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds. © 2006 Springer Science+Business Media, Inc.

AB - We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some ? > 0 to a subclass of the class S ? (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the "spatially local" asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds. © 2006 Springer Science+Business Media, Inc.

KW - Exact asymptotics

KW - Ruin probability

KW - Supremum of random walk

UR - http://www.scopus.com/inward/record.url?scp=33845504874&partnerID=8YFLogxK

U2 - 10.1007/s11202-006-0112-8

DO - 10.1007/s11202-006-0112-8

M3 - Article

VL - 47

SP - 1034

EP - 1041

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -