Publikation: Stable processes with reflections
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2025
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Bogdan, Krzysztof
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Stochastic Processes and their Applications. Elsevier. 2025, 187, 104654. ISSN 0304-4149. eISSN 1879-209X. VerfĂŒgbar unter: doi: 10.1016/j.spa.2025.104654
Zusammenfassung
We construct a Hunt process that can be described as an isotropic đŒ-stable LĂ©vy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes. It is based on nonlocal Schrödinger perturbations of sub-Markovian transition kernels and the construction of two supermedian functions with different growth rates at infinity. We apply this framework to describe the return distribution and the stationary distribution of the process. To handle the strong Markov property at the reflection time, we introduce a novel ladder process, whose transition semigroup encodes not only the position of the process, but also the number of reflections.
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510 Mathematik
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BOGDAN, Krzysztof, Markus KUNZE, 2025. Stable processes with reflections. In: Stochastic Processes and their Applications. Elsevier. 2025, 187, 104654. ISSN 0304-4149. eISSN 1879-209X. VerfĂŒgbar unter: doi: 10.1016/j.spa.2025.104654BibTex
@article{Bogdan2025-09Stabl-73612,
title={Stable processes with reflections},
year={2025},
doi={10.1016/j.spa.2025.104654},
volume={187},
issn={0304-4149},
journal={Stochastic Processes and their Applications},
author={Bogdan, Krzysztof and Kunze, Markus},
note={Article Number: 104654}
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