2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209687In 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.Probability60G18, 60G51, 60B52text