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On the maximal displacement of some critical branching Lévy processes with stable offspring distribution.

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Title: On the maximal displacement of some critical branching Lévy processes with stable offspring distribution.
Authors: Profeta, Christophe1 (AUTHOR) christophe.profeta@univ-evry.fr
Source: Stochastic Processes & Their Applications. Jun2026, Vol. 196, pN.PAG-N.PAG. 1p.
Subjects: Lévy processes, Branching processes, Distribution (Probability theory), Probability theory
Abstract: Let X be a critical branching Lévy 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 Lévy 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. [ABSTRACT FROM AUTHOR]
Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192588955
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the maximal displacement of some critical branching Lévy processes with stable offspring distribution.
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  Data: <searchLink fieldCode="AR" term="%22Profeta%2C+Christophe%22">Profeta, Christophe</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> christophe.profeta@univ-evry.fr</i>
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  Data: <searchLink fieldCode="DE" term="%22Lévy+processes%22">Lévy processes</searchLink><br /><searchLink fieldCode="DE" term="%22Branching+processes%22">Branching processes</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink>
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  Label: Abstract
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  Data: Let X be a critical branching Lévy 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 Lévy 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.spa.2026.104921
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Lévy processes
        Type: general
      – SubjectFull: Branching processes
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Probability theory
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      – TitleFull: On the maximal displacement of some critical branching Lévy processes with stable offspring distribution.
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 196
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