## Electronic Communications in Probability

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

#### 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).

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 63, 720-731.

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

https://projecteuclid.org/euclid.ecp/1465262019

Digital Object Identifier
doi:10.1214/ECP.v16-1679

Mathematical Reviews number (MathSciNet)
MR2861436

Zentralblatt MATH identifier
1245.60079

Rights

#### Citation

Pardoux, Etienne; Wakolbinger, Anton. From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth. Electron. Commun. Probab. 16 (2011), paper no. 63, 720--731. doi:10.1214/ECP.v16-1679. https://projecteuclid.org/euclid.ecp/1465262019

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