Non-binary branching process and non-Markovian exploration process

Ibrahima Dramé (1, 2) , Etienne Pardoux (1) , Ahmadou Bamba Sow (2)

1 I2M - Institut de Mathématiques de Marseille
2 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement

We study both a continuous time non-binary Galton−Watson random tree and its explo- ration (or height) process in the subcritical, critical and supercritical cases. We then renormalize our branching process and exploration process, and take the weak limit as the size of the population tends to infinity.

Mots clés: local time; weak limit; Branching process; exploration process

Domaines: Mathématiques [math]; Probabilités [math.PR]

Ibrahima Dramé, Etienne Pardoux, Ahmadou Bamba Sow. Non-binary branching process and non-Markovian exploration process. ESAIM: Probability and Statistics, 2017, 21, pp.1 - 33. ⟨10.1051/ps/2016027⟩. ⟨hal-01516048⟩