Complete monotonicity of time-changed Lévy processes at first passage

Matija Vidmar

Statistics & Probability Letters, 2023, vol. 193, issue C

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.

Keywords: Spectrally positive Lévy process; Time-change; First passage; Complete monotonicity; Laplace transform (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109710

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