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The empirical mean position of a branching Lévy process

Part of: Markov processes

Published online by Cambridge University Press:  23 November 2020

David Cheek  and
Seva Shneer
David Cheek*
Affiliation:
Harvard University
Seva Shneer*
Affiliation:
Harvard University
*
*Postal address: Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, USA. Email address: dmcheek@g.harvard.edu
**Postal address: School of MACS, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email address: v.shneer@hw.ac.uk
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Abstract

We consider a supercritical branching Lévy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit theorem on the empirical mean position.

Keywords

Branching Lévy processbranching random walkbranching Brownian motionempirical mean positionempirical mean depth

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1252 - 1259
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Copyright
© Applied Probability Trust 2020

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