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

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

2004-12-16

arxiv.org/abs/math/0412322v1

Mathematics

Probability

Scientific paper

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.

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