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2011 From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth
Etienne Pardoux, Anton Wakolbinger
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Electron. Commun. Probab. 16: 720-731 (2011). DOI: 10.1214/ECP.v16-1679

Abstract

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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Etienne Pardoux. Anton Wakolbinger. "From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth." Electron. Commun. Probab. 16 720 - 731, 2011. https://doi.org/10.1214/ECP.v16-1679

Information

Accepted: 20 November 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1245.60079
MathSciNet: MR2861436
Digital Object Identifier: 10.1214/ECP.v16-1679

Subjects:
Primary: 60J70
Secondary: 60H10, 60J55, 60J80

JOURNAL ARTICLE
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