A new approximation of the Height process of a CSBP

2020/03/11 by Ibrahima Dramé, Drame, Ibrahima
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2003.05329

Abstract

We code Galton-Walton trees by a continuous height process, in order to give a precise meaning to the convergence of forests of trees. This allows us to establish the convergence of the forest of genealogical trees of the branching process of a large population towards the genealogical trees of the limiting continuous state branching process (CSBP). The approximation considered here is new, compared to that which has been studied in Etienne Pardoux.

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