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arXiv · 0712.0987

On continuous state branching processes: conditioning and self-similarity

A. E. Kyprianou·J. C. Pardo
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Abstract

In this paper, for $α\in (1, 2}$ we show that the $α$-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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A. E. Kyprianou, J. C. Pardo. 2007-12-06. On continuous state branching processes: conditioning and self-similarity. https://arxiv.org/abs/0712.0987

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