On continuous state branching processes: conditioning and self-similarity
Probability
2008-12-08 v1
Abstract
In this paper, for \alpha\in (1, 2} we show that the -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.
Keywords
Cite
@article{arxiv.0712.0987,
title = {On continuous state branching processes: conditioning and self-similarity},
author = {A. E. Kyprianou and J. C. Pardo},
journal= {arXiv preprint arXiv:0712.0987},
year = {2008}
}