Local asymptotics of the cycle maximum of a heavy-tailed random walk

Authors
Denisov, Denis Shneer, Vsevolod
Citation
Denisov, Denis et Shneer, Vsevolod, Local asymptotics of the cycle maximum of a heavy-tailed random walk, Advances in applied probability , 39(1), 2007, pp. 221-244
Journal title
Advances in applied probability → ACNP
ISSN journal
00018678
Volume
39
Issue
1
Year of publication
2007
Pages
221 - 244
Database
ACNP
SICI code
Abstract
Let ., .1, .2,. be a sequence of independent and identically distributed random variables, and let Sn=.1+.+.n and Mn=maxk.nSk. Let .=min{n.1: Sn.0}. We assume that . has a heavy-tailed distribution and negative, finite mean E(.)<0. We find the asymptotics of P{M. . (x, x+T]} as x.., for a fixed, positive constant T.