On continuous state branching processes: conditioning and self-similarity

Abstract

In this paper, for $α\in (1, 2}$ 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.

References in corpus (2)

• Recurrent extensions of self-similar Markov processes and Cramér's condition II
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes

Cited by in corpus (1)

• On the Lamperti stable processes