Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions

Jean Bertoin (1) , Bernard Roynette (2) , Marc Yor (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IECN - Institut Élie Cartan de Nancy

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to x^{\alpha}$ where $x\geq0$ and $0<\alpha\leq 1/2$, and in particular the critical parameter $\alpha=1/2$, play a distinguished role.

Mots clés: Bernstein function; branching mechanism; subordination; stable process

Domaines: Probabilités [math.PR]

Jean Bertoin, Bernard Roynette, Marc Yor. Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions. 2004. ⟨hal-00003605⟩