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

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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 ${\bf e}_\alpha: x\to x^{\alpha}$ 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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hal-00003605 , version 1 (16-12-2004)

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