$α$-stable Lévy processes entering the half space or a slab
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arXiv
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| Format: | Preprint |
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2024
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| author | Kyprianou, Andreas E. Medina, Sonny Pardo, Juan Carlos |
| author_facet | Kyprianou, Andreas E. Medina, Sonny Pardo, Juan Carlos |
| contents | Recent fluctuation identities for $α$-stable Lévy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory can be exploited. Inspired by this approach, we give a different decomposition of the $d$-dimensional isotropic $α$-stable Lévy processes in terms of orthogonal coordinates. Accordingly we are able to develop a number of $n$-tuple laws for first entrance into a half-space. We also numerically construct the law of first entry of the process into a slab of the form $(-1, 1)\times \mathbb{R}^{d-1}$ using a walk-on-half-spaces Monte Carlo approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $α$-stable Lévy processes entering the half space or a slab Kyprianou, Andreas E. Medina, Sonny Pardo, Juan Carlos Probability 60G18, 60G52, 60G51 Recent fluctuation identities for $α$-stable Lévy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory can be exploited. Inspired by this approach, we give a different decomposition of the $d$-dimensional isotropic $α$-stable Lévy processes in terms of orthogonal coordinates. Accordingly we are able to develop a number of $n$-tuple laws for first entrance into a half-space. We also numerically construct the law of first entry of the process into a slab of the form $(-1, 1)\times \mathbb{R}^{d-1}$ using a walk-on-half-spaces Monte Carlo approach. |
| title | $α$-stable Lévy processes entering the half space or a slab |
| topic | Probability 60G18, 60G52, 60G51 |
| url | https://arxiv.org/abs/2407.20394 |