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

Jean Bertoin·Bernard Roynette·Marc Yor
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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 ${\bf e}_α: x\to x^α$ where $x\geq0$ and $0<α\leq 1/2$, and in particular the critical parameter $α=1/2$, play a distinguished role.

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Jean Bertoin, Bernard Roynette, Marc Yor. 2004-12-16. Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions. https://arxiv.org/abs/math/0412322

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