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2018 The genealogy of an exactly solvable Ornstein–Uhlenbeck type branching process with selection
Aser Cortines, Bastien Mallein
Electron. Commun. Probab. 23: 1-13 (2018). DOI: 10.1214/18-ECP197

Abstract

We study the genealogy of an exactly solvable population model with $N$ particles on the real line, which evolves according to a discrete-time branching process with selection. At each time step, every particle gives birth to children around $a$ times its current position, where $a>0$ is a parameter of the model. Then, the $N$ rightmost newborn children are selected to form the next generation. We show that the genealogy of the process converges toward a Beta coalescent as $N \to \infty $. The process we consider can be seen as a toy model version of a continuous-time branching process with selection, in which particles move according to independent Ornstein–Uhlenbeck processes. The parameter $a$ is akin to the pulling strength of the Ornstein–Uhlenbeck process.

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Aser Cortines. Bastien Mallein. "The genealogy of an exactly solvable Ornstein–Uhlenbeck type branching process with selection." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP197

Information

Received: 6 February 2018; Accepted: 19 November 2018; Published: 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07023484
MathSciNet: MR3896836
Digital Object Identifier: 10.1214/18-ECP197

Subjects:
Primary: 60K35, S0J80
Secondary: 92D15

JOURNAL ARTICLE
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