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Article Dans Une Revue Electronic Communications in Probability Année : 2011

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

Résumé

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 \cite{LPW}, 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 \cite{NRW}.

Dates et versions

hal-01231988 , version 1 (21-11-2015)

Identifiants

Citer

Etienne Pardoux, Anton Wakolbinger. From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth. Electronic Communications in Probability, 2011, 16, pp.720-731. ⟨10.1214/ECP.v16-1679⟩. ⟨hal-01231988⟩
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