The structure of entrance and exit at infinity for time-changed Lévy processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929535508807680 |
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| author | Baguley, Samuel Döring, Leif Shi, Quan |
| author_facet | Baguley, Samuel Döring, Leif Shi, Quan |
| contents | Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different discontinuous Markov processes in the past two decades. Proofs often use time-change techniques and rely on problem specific knowledge such branching or scaling properties. In this article we ask how far techniques can be pushed with as little as possible model assumptions. We give sharp conditions on time-changed Lévy processes to allow entrance and regular boundary point at infinity. The main tool we introduce is a generalised scaling property that holds for all time-changed Lévy processes and can be used to extend scaling arguments for self-similar Markov processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The structure of entrance and exit at infinity for time-changed Lévy processes Baguley, Samuel Döring, Leif Shi, Quan Probability 60G51, 60G18, 60J50 Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different discontinuous Markov processes in the past two decades. Proofs often use time-change techniques and rely on problem specific knowledge such branching or scaling properties. In this article we ask how far techniques can be pushed with as little as possible model assumptions. We give sharp conditions on time-changed Lévy processes to allow entrance and regular boundary point at infinity. The main tool we introduce is a generalised scaling property that holds for all time-changed Lévy processes and can be used to extend scaling arguments for self-similar Markov processes. |
| title | The structure of entrance and exit at infinity for time-changed Lévy processes |
| topic | Probability 60G51, 60G18, 60J50 |
| url | https://arxiv.org/abs/2410.07664 |