First passage upwards for state-dependent-killed spectrally negative Lévy processes. (June 2019)

• Record Type: Journal Article
• Authors: Vidmar, Matija
• Is Part Of: Journal of applied probability. Volume 56:Number 2(2019)
• Page Start: 472
• Page End: 495
• Publication Date: 2019-06
• Subjects: Spectrally negative Lévy process, -- first passage upwards, -- killing, -- time change; Primary 60G51, -- Secondary 60J25, -- 60G44; 519.2
• DOI: 10.1017/jpr.2019.23
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: For a spectrally negative Lévy process X, killed according to a rate that is a function ω of its position, we complement the recent findings of [12 ] by analysing (in greater generality) the exit probability of the one-sided upwards passage problem. When ω is strictly positive, this problem is related to the determination of the Laplace transform of the first passage time upwards for X that has been time-changed by the inverse of the additive functional $$\int_0^ \cdot \omega ({X_u}){\kern 1pt} {\rm{d}}u$$ . In particular, our findings thus shed extra light on related results concerning first passage times downwards (resp. upwards) of continuous-state branching processes (resp. spectrally negative positive self-similar Markov processes).