On continuous state branching processes: conditioning and self-similarity

Details On continuous state branching processes: conditioning and self-similarity On continuous state branching processes: conditioning and self-similarity

2007-12-06

arxiv.org/abs/0712.0987v1

Mathematics

Probability

Scientific paper

In this paper, for $\alpha\in (1, 2}$ we show that the $\alpha$-stable continuous-state branching process and the associated process conditioned never to become extinct are positive self-similar Markov processes. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive self-similar Markov processes permits accessto a number of explicit results concerning the paths of stable-continuous branching processes and its conditioned version.

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