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2019 Coalescences in continuous-state branching processes
Clément Foucart, Chunhua Ma, Bastien Mallein
Electron. J. Probab. 24: 1-52 (2019). DOI: 10.1214/19-EJP358

Abstract

Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes with negative jumps, which correspond to the ancestral lineages of individuals in the current generation. The process of the ancestral lineage of a fixed individual is the Siegmund dual process of the continuous-state branching process. We study its semi-group, its long-term behaviour and its generator. In order to follow the coalescences in the ancestral lineages and to describe the backward genealogy of the population, we define non-exchangeable Markovian coalescent processes obtained by sampling individuals according to an independent Poisson point process over the flow. These coalescent processes are called consecutive coalescents, as only consecutive blocks can merge. They are characterized in law by finite measures on $\mathbb{N} $ which can be thought as the offspring distributions of some inhomogeneous immortal Galton-Watson processes forward in time.

Citation

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Clément Foucart. Chunhua Ma. Bastien Mallein. "Coalescences in continuous-state branching processes." Electron. J. Probab. 24 1 - 52, 2019. https://doi.org/10.1214/19-EJP358

Information

Received: 17 January 2019; Accepted: 8 September 2019; Published: 2019
First available in Project Euclid: 1 October 2019

zbMATH: 07142897
MathSciNet: MR4017121
Digital Object Identifier: 10.1214/19-EJP358

Subjects:
Primary: 60J25, 60J27, 60J28, 60J80

JOURNAL ARTICLE
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Vol.24 • 2019
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