Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 63, 720-731.
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).
Electron. Commun. Probab., Volume 16 (2011), paper no. 63, 720-731.
Accepted: 20 November 2011
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 60J55: Local time and additive functionals 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60H10: Stochastic ordinary differential equations [See also 34F05]
This work is licensed under aCreative Commons Attribution 3.0 License.
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