Lévy processes with partially stochastic resetting
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910270054465536 |
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| author | Palmowski, Zbigniew Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. |
| author_facet | Palmowski, Zbigniew Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. |
| contents | In this paper, we solve exit problems for a Lévy process that resets proportionally to its current position at independent Poisson epochs times. This resetting causes an additional (proportional to its current level) downward (upward) jump when the current position of the process is on the positive (negative) domain. Such a process can be expressed as an SDE, whose existence and uniqueness it discussed. All identities are given in terms of new family of
scale functions. To obtain the new family of scale functions, we reduce the problem of the LT of the exit times into integral equations that are solve in terms of resolvent series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18136 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lévy processes with partially stochastic resetting Palmowski, Zbigniew Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. Probability In this paper, we solve exit problems for a Lévy process that resets proportionally to its current position at independent Poisson epochs times. This resetting causes an additional (proportional to its current level) downward (upward) jump when the current position of the process is on the positive (negative) domain. Such a process can be expressed as an SDE, whose existence and uniqueness it discussed. All identities are given in terms of new family of scale functions. To obtain the new family of scale functions, we reduce the problem of the LT of the exit times into integral equations that are solve in terms of resolvent series. |
| title | Lévy processes with partially stochastic resetting |
| topic | Probability |
| url | https://arxiv.org/abs/2605.18136 |