Ray-Knight representation of flows of branching processes with\n competition by pruning of L 'evy trees

2015/05/29 by Julien Berestycki, Berestycki, Julien, María Clara Fittipaldi +3 · 3 citations
Economics, Econometrics and Finance · Mathematics · Medicine · #60G57 #60J25 #60J80 #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1506.00046

openalex publication_date 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce flows of branching processes with competition, which describe\nthe evolution of general continuous state branching populations in which\ninteractions between individuals give rise to a negative density dependence\nterm. This generalizes the logistic branching processes studied by Lambert.\nFollowing the approach developed by Dawson and Li, we first construct such\nprocesses as the solutions of certain flow of stochastic differential\nequations. We then propose a novel genealogical description for branching\nprocesses with competition based on interactive pruning of L 'evy-trees, and\nestablish a Ray-Knight representation result for these processes in terms of\nthe local times of suitably pruned forests.\n

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