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

Ibrahima Drame; Etienne Pardoux

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arXiv · 1706.05747

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

Ibrahima Drame·Etienne Pardoux

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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 L\'evy processes : The exploration process".

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Ibrahima Drame, Etienne Pardoux. 2017-06-19. Convergence to a Continuous State Branching Process with jumps and Height Process. https://arxiv.org/abs/1706.05747

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