Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions
Abstract
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
e
α
:x→
x
α
where
x≥0
and
0<α≤1/2
, and in particular the critical parameter
α=1/2
, play a distinguished role.