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On the genealogy of branching populations and their diffusion limits

Part of: Markov processes

Published online by Cambridge University Press:  01 February 2019

Olav Kallenberg
Olav Kallenberg*
Affiliation:
Auburn University
*
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USA. Email address: kalleoh@auburn.edu
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Abstract

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We consider the evolution of the ancestral structure of a classical branching process in space and its diffusion limit. We also indicate how the conditional structure of the past can be described asymptotically in terms of suitable uniform Brownian trees.

Keywords

Branching trees and processesgenealogysuperprocess

MSC classification

Primary: 60J68: Superprocesses
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 173 - 176
Copyright
Copyright © Applied Probability Trust 2018 

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