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A stable Langevin model with diffusive-reflective boundary conditions.

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Title: A stable Langevin model with diffusive-reflective boundary conditions.
Authors: Jabir, Jean-François1 (AUTHOR) jjabir@hse.ru, Profeta, Christophe2 (AUTHOR) christophe.profeta@univ-evry.fr
Source: Stochastic Processes & Their Applications. Nov2019, Vol. 129 Issue 11, p4269-4293. 25p.
Subjects: Lévy processes, Brownian motion, Legal education, Wiener processes
Abstract: In this note, we consider the construction of a one-dimensional stable Langevin type process confined in the upper half-plane and submitted to diffusive-reflective boundary conditions whenever the particle position hits 0. We show that two main different regimes appear according to the values of the chosen parameters. We then use this study to construct the law of a (free) stable Langevin process conditioned to stay positive, thus extending earlier works on integrated Brownian motion. This construction further allows to obtain the exact asymptotics of the persistence probability of the integrated stable Lévy process. In addition, the paper is concluded by solving the associated trace problem in the symmetric case. [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: 138888932
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  Data: A stable Langevin model with diffusive-reflective boundary conditions.
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  Data: <searchLink fieldCode="AR" term="%22Jabir%2C+Jean-François%22">Jabir, Jean-François</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jjabir@hse.ru</i><br /><searchLink fieldCode="AR" term="%22Profeta%2C+Christophe%22">Profeta, Christophe</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> christophe.profeta@univ-evry.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Stochastic+Processes+%26+Their+Applications%22">Stochastic Processes & Their Applications</searchLink>. Nov2019, Vol. 129 Issue 11, p4269-4293. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Lévy+processes%22">Lévy processes</searchLink><br /><searchLink fieldCode="DE" term="%22Brownian+motion%22">Brownian motion</searchLink><br /><searchLink fieldCode="DE" term="%22Legal+education%22">Legal education</searchLink><br /><searchLink fieldCode="DE" term="%22Wiener+processes%22">Wiener processes</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this note, we consider the construction of a one-dimensional stable Langevin type process confined in the upper half-plane and submitted to diffusive-reflective boundary conditions whenever the particle position hits 0. We show that two main different regimes appear according to the values of the chosen parameters. We then use this study to construct the law of a (free) stable Langevin process conditioned to stay positive, thus extending earlier works on integrated Brownian motion. This construction further allows to obtain the exact asymptotics of the persistence probability of the integrated stable Lévy process. In addition, the paper is concluded by solving the associated trace problem in the symmetric case. [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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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.spa.2018.11.020
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 25
        StartPage: 4269
    Subjects:
      – SubjectFull: Lévy processes
        Type: general
      – SubjectFull: Brownian motion
        Type: general
      – SubjectFull: Legal education
        Type: general
      – SubjectFull: Wiener processes
        Type: general
    Titles:
      – TitleFull: A stable Langevin model with diffusive-reflective boundary conditions.
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            NameFull: Jabir, Jean-François
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            NameFull: Profeta, Christophe
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            – D: 01
              M: 11
              Text: Nov2019
              Type: published
              Y: 2019
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              Value: 129
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              Value: 11
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            – TitleFull: Stochastic Processes & Their Applications
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