On the maximal displacement of some critical branching L{é}vy processes with stable offspring distribution
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866912290239938560 |
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| author | Profeta, Christophe |
| author_facet | Profeta, Christophe |
| contents | Let X be a critical branching L{é}vy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different situations: first when the underlying L{é}vy process L admits moments of order at least two and is not centered, and then when the distribution of L has a regularly varying tail. This work complements some earlier results in which either L was centered or the offspring distribution was assumed to have moments of order three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the maximal displacement of some critical branching L{é}vy processes with stable offspring distribution Profeta, Christophe Probability Let X be a critical branching L{é}vy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different situations: first when the underlying L{é}vy process L admits moments of order at least two and is not centered, and then when the distribution of L has a regularly varying tail. This work complements some earlier results in which either L was centered or the offspring distribution was assumed to have moments of order three. |
| title | On the maximal displacement of some critical branching L{é}vy processes with stable offspring distribution |
| topic | Probability |
| url | https://arxiv.org/abs/2503.18451 |