Electronic Communications in Probability

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

Etienne Pardoux and Anton Wakolbinger

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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

Permanent link to this document
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

Subjects
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]

Keywords
Ray-Knight representation local time Feller branching with logistic growth Brownian motion local time drift Girsanov transform

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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References

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