From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth

  • We give a new proof for a Ray-Knight representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. In Le et al. (2011) such a representation was obtained by an approximation through Harris paths that code the genealogies of particle systems. The present proof is purely in terms of stochastic analysis, and is inspired by previous work of Norris, Rogers and Williams (1988).

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Metadaten
Author:Etienne Pardoux, Anton WakolbingerGND
URN:urn:nbn:de:hebis:30:3-403463
URL:http://ecp.ejpecp.org/article/view/1679
DOI:https://doi.org/10.1214/ECP.v16-1679
ISSN:1083-589X
Parent Title (German):Electronic communications in probability
Publisher:EMIS ELibEMS
Place of publication:[Madralin]
Document Type:Article
Language:English
Year of Completion:2011
Year of first Publication:2011
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2016/06/02
Tag:Brownian motion; Feller branching with logistic growth; Girsanov transform; Ray-Knight representation; local time; local time drift
Volume:16
Page Number:12
First Page:720
Last Page:731
Note:
This work is licensed under a Creative Commons Attribution 3.0 License.
HeBIS-PPN:428603475
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J55 Local time and additive functionals
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 3.0

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