arXiv subjects

Ibrahima Dramé

Publications and source records attributed to Ibrahima Dramé.

2 recordsLinked to original sources

arXiv2025

Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes

We establish a Law of Large Numbers and a Central Limit Theorem for a class of Crump Mode Jagers continuous time branching processes, where the birth rate is age dependent, and also random (different from one individual to the next), in the limit of a large number of ancestors. The only difficulty concerns the tightness in the Skorohod space $D$ for the central limit theorem. We exploit a criterion for the CLT in $D$ due to M. Hahn \cite{MH}.

math.PR↗

arXiv2016

Non-binary branching process and Non-Markovian exploration process

We study the exploration (or height) process of a continuous time non-binary Galton-Watson random tree, in the subcritical, critical and supercritical cases. Thus we consider the branching process in continuous time (Z_{t})_{t\geq 0}, which describes the number of offspring alive at time t. We then renormalize our branching process and exploration process, and take the weak limit as the size of the population tends to infinity. Finally we deduce a Ray-Knight representation.

math.PR↗