On the limit law of a random walk conditioned to reach a high level

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Foss, Sergey G.^1,2  Puhalskii, Anatolii A.^3,4 

[1] Heriot Watt Univ, Edinburgh, Midlothian, Scotland

[2] Russian Acad Sci, Inst Math, Novosibirsk 630090, Russia

[3] Univ Colorado, Denver, CO 80202 USA

[4] Russian Acad Sci, Inst Problems Informat Transmiss, Moscow, Russia

关键词: Random walk with negative drift;    Tail asymptotics for the supremum;    Borderline case;    Convergence of conditional laws;    Spectrally positive Levy process conditioned not to overshoot;   

DOI  :  10.1016/j.spa.2010.10.007

来源: Elsevier

【 摘 要 】

We consider a random walk with a negative drift and with a jump distribution which under Cramer's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Levy process conditioned not to overshoot level 1. (c) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free