A path-valued Markov process indexed by the ancestral mass - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2015

A path-valued Markov process indexed by the ancestral mass

Résumé

A family of Feller branching diffusions $Z^x$, $x \ge 0$, with nonlinear drift and initial value $x$ can, with a suitable coupling over the {\em ancestral masses} $x$, be viewed as a path-valued process indexed by $x$. For a coupling due to Dawson and Li, which in case of a linear drift describes the corresponding Feller branching diffusion, and in our case makes the path-valued process Markovian, we find an SDE solved by $Z$, which is driven by a random point measure on excursion space. In this way we are able to identify the infinitesimal generator of the path-valued process. We also establish path properties of $x\mapsto Z^x$ using various couplings of $Z$ with classical Feller branching diffusions.

Dates et versions

hal-01231771 , version 1 (20-11-2015)

Identifiants

Citer

Etienne Pardoux, Anton Wakolbinger. A path-valued Markov process indexed by the ancestral mass. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2015, 12 (1), pp.193-212. ⟨hal-01231771⟩
101 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More