On reflected Lévy processes with collapse
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915105558495232 |
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| author | Boxma, Onno Kella, Offer Perry, David |
| author_facet | Boxma, Onno Kella, Offer Perry, David |
| contents | We consider a Lévy process reflected at the origin with additional i.i.d. collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the Lévy process is spectrally positive and finally we specialize further to the two cases where the Lévy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On reflected Lévy processes with collapse Boxma, Onno Kella, Offer Perry, David Probability 60G51 We consider a Lévy process reflected at the origin with additional i.i.d. collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the Lévy process is spectrally positive and finally we specialize further to the two cases where the Lévy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope. |
| title | On reflected Lévy processes with collapse |
| topic | Probability 60G51 |
| url | https://arxiv.org/abs/2501.09365 |