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Complete monotonicity of time-changed Lévy processes at first passage

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  • Vidmar, Matija

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.

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  • Vidmar, Matija, 2023. "Complete monotonicity of time-changed Lévy processes at first passage," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002231
    DOI: 10.1016/j.spl.2022.109710
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    References listed on IDEAS

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    1. Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
    2. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    3. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.
    4. F. Avram & P. Patie & J. Wang, 2019. "Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 391-399, June.
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    1. Foucart, Clément & Vidmar, Matija, 2024. "Continuous-state branching processes with collisions: First passage times and duality," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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