Convergence to a Continuous State Branching Process with jumps and Height Process

2017/06/19 by Ibrahima Dramé, Drame, Ibrahima, Étienne Pardoux +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1706.05747

openalex publication_date 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study asymptotics of the genealogy of Galton-Watson processes. Thus we consider a offspring distribution such that the rescaled Galton-Watson processes converges to a continuous state branching process (CSBP) with jumps. After we show that the rescaled height (or exploration) process of the corresponding Galton-Watson family tree, converges in a functional sense, to the continuous height process that Le Gall and Le Jan introduced in 1998 on their paper "branching processes in Lévy processes : The exploration process".

Citations

• Stochastic equations of non-negative processes with jumps

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