First passage upwards for state dependent-killed spectrally negative Lévy processes

2018/03/13 by Vidmar, Matija
#60G44 #FOS: Mathematics #Primary: 60G51 #Probability (math.PR) #Secondary: 60J25

paper · doi:10.48550/arxiv.1803.04885

Abstract

For a spectrally negative Lévy process (snLp) X, killed according to a rate that is a function ω of its position, we analyse 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 ∫₀^⋅ ω(X_u)du. In particular our findings thus shed extra light on related results concerning first passage times upwards (downwards) of spectrally negative positive self-similar Markov processes (continuous state branching processes).

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