Theory of Probability and Mathematical Statistics
Approximation of the height process of a continuous state branching process with interaction
I. Drame, E. Pardoux
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Abstract: We first show that the properly rescaled height process of the genealogical tree of a continuous time branching process converges to the height process of the genealogy of a (possibly discontinuous) continuous state branching process. We then prove the same type of result for generalized branching processes with interaction.
Keywords: Continuous-State Branching Processes; Scaling Limit; Galton-Watson Processes; Lévy Processes; Local time; height process
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