First passage times for subordinate Brownian motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Kwasnicki, Mateusz^1,2  Malecki, Jacek^1,3  Ryznar, Michal¹ 

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

[2] Polish Acad Sci, Inst Math, PL-00976 Warsaw, Poland

[3] Univ Angers, LAREMA, F-49045 Angers 1, France

关键词: Levy process;    Subordinate process;    First passage time;    Supremum functional;   

DOI  :  10.1016/j.spa.2013.01.011

来源: Elsevier

【 摘 要 】

Let X-t be a subordinate Brownian motion, and suppose that the Levy measure of the underlying subordinator has a completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(tau(x) > t) of first passage times tau(x) through a barrier at x > 0, and its derivatives in t. As a corollary, we examine the asymptotic behaviour of P(tau(x) > t) and its t-derivatives, either as t -> infinity or x -> 0(+). (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free