General branching processes as Markov fields
type: Item
instance of: scholarly article
title: General branching processes as Markov fields
zbMATH Open document ID: 0678.92009
DOI: 10.1016/0304-4149(89)90075-6
author: P. Jagers
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: The evolution of newborns in general branching processes with abstract type space are dependent on types from their mothers and independent of the history of their earlier ancestry. This leads to Markov fields on the space of sets of individuals, partially ordered by descent. The structure of such fields is investigated by martingale and Markov renewal methods. These results are used for proofs on the limit theorems for a normalized spread-out supercritical Malthusian population.
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4112442
zbMATH Keywords: strong Markov property
zbMATH Keywords: intrinsic martingale
zbMATH Keywords: population growth
zbMATH Keywords: population genetics
zbMATH Keywords: evolution of newborns
zbMATH Keywords: general branching processes
zbMATH Keywords: abstract type space
zbMATH Keywords: Markov fields
zbMATH Keywords: Markov renewal methods
zbMATH Keywords: supercritical Malthusian population
reviewed by: Valentin Topchii
MaRDI profile type: Publication
full work available at URL: 0304-4149(89)90075-6
OpenAlex ID: W2041237873
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description: scientific article; zbMATH DE number 4112442