α-stable Lévy processes entering the half space or a slab

Andreas E. Kyprianou, Sonny Medina and Juan Carlos Pardo

Stochastic Processes and their Applications, 2025, vol. 186, issue C

Abstract: Recently a series of publications, including e.g. (Kyprianou, 2016 [1]; Kyprianou et al., 2018 [2]; Kyprianou et al., 2019; Kyprianou et al., 2014; Kyprianou and Pardo, 2022), considered a number of new fluctuation identities for α-stable Lévy processes in one and higher dimensions by appealing to underlying Lamperti-type path decompositions. In the setting of d-dimensional isotropic processes, (Kyprianou et al., 2019) in particular, developed so called n-tuple laws for first entrance and exit of balls. Fundamental to these works is the notion that the paths can be decomposed via generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory (in the sense of Maisonneuve (1975)) can be exploited.

Keywords: Stable processes; First passage problems; Walk-on-spheres Monte Carlo (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104644

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