Supercritical multitype branching processes: the ancestral types of typical individuals
H. Georgii, and E. Baake. Adv. in Appl. Probab., 35 (4):
1090--1110(2003)
Abstract
For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a `conceptual proof' (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.
%0 Journal Article
%1 georgii2003ancestral
%A Georgii, Hans-Otto
%A Baake, Ellen
%D 2003
%J Adv. in Appl. Probab.
%K ancestral_process branching_processes large_deviations selection
%N 4
%P 1090--1110
%T Supercritical multitype branching processes: the ancestral types of typical individuals
%U http://dx.doi.org/10.1239/aap/1067436336
%V 35
%X For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a `conceptual proof' (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.
@article{georgii2003ancestral,
abstract = {For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a `conceptual proof' (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem. },
added-at = {2010-10-26T01:18:06.000+0200},
author = {Georgii, Hans-Otto and Baake, Ellen},
biburl = {https://www.bibsonomy.org/bibtex/2f69d01f059f56174c0eca260364a5d5b/peter.ralph},
coden = {AAPBBD},
fjournal = {Advances in Applied Probability},
interhash = {1e6c16b7d9b64a21eeb38ecd066ec00a},
intrahash = {f69d01f059f56174c0eca260364a5d5b},
issn = {0001-8678},
journal = {Adv. in Appl. Probab.},
keywords = {ancestral_process branching_processes large_deviations selection},
mrclass = {60J80 (60F10)},
mrnumber = {MR2014271 (2005a:60132)},
mrreviewer = {Ingemar Kaj},
number = 4,
pages = {1090--1110},
timestamp = {2010-10-26T01:18:06.000+0200},
title = {Supercritical multitype branching processes: the ancestral types of typical individuals},
url = {http://dx.doi.org/10.1239/aap/1067436336},
volume = 35,
year = 2003
}