Height process for super-critical continuous state branching process

2006/11/07 by Jean‐François Delmas, Delmas, Jean-François
Mathematics · Physics and Astronomy · #60J55 #60J65 #60J80 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.math/0611172

openalex publication_date 2006/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity. Then we extend the pruning procedure of branching processes to the super-critical case. This give a complete duality picture between pruning and size proportional immigration for quadratic continuous state branching processes.

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