Complete monotonicity of time-changed Lévy processes at first passage

2022/05/13 by Matija Vidmar, Vidmar, Matija
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60G51 #Advanced Queuing Theory Analysis #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2205.06654

openalex publication_date 2022/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the class of (possibly killed) spectrally positive Lévy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following property: as functions of point of issue, the Laplace transforms of their first-passage times downwards are completely monotone. A wide (dense, in a sense) subfamily of this family admits closed form expressions for said Laplace transforms.

Related

• First passage upwards for state dependent-killed spectrally negative Lévy processes
• Time-changed spectrally positive Lévy processes starting from infinity
• Integral transforms related to Nevanlinna-Pick functions from an analytic, probabilistic and free-probability point of view
• Levy Processes: Hitting time, overshoot and undershoot - part I: Functional equations
• Suprema of Lévy processes with completely monotone jumps: spectral-theoretic approach