Asymptotic genealogy of a critical branching process
L. Popovic. Ann. Appl. Probab., 14 (4):
2120--2148(2004)arxiv:math/0503577.
Аннотация
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.
Описание
MR: Publications results for "MR Number=(2100386)"
%0 Journal Article
%1 MR2100386
%A Popovic, Lea
%D 2004
%J Ann. Appl. Probab.
%K branching_processes continuous-state_branching_processes genealogies
%N 4
%P 2120--2148
%T Asymptotic genealogy of a critical branching process
%U http://www.projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.aoap/1099674091&page=record
%V 14
%X Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.
@article{MR2100386,
abstract = {Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution. },
added-at = {2009-01-15T22:27:19.000+0100},
author = {Popovic, Lea},
biburl = {https://www.bibsonomy.org/bibtex/2397be78fdc4a08838c7cbc3b2f7fd5a0/peter.ralph},
description = {MR: Publications results for "MR Number=(2100386)"},
fjournal = {The Annals of Applied Probability},
interhash = {4e64b1c67f5b1f8d77db0b27d7c2fc85},
intrahash = {397be78fdc4a08838c7cbc3b2f7fd5a0},
issn = {1050-5164},
journal = {Ann. Appl. Probab.},
keywords = {branching_processes continuous-state_branching_processes genealogies},
mrclass = {60J85 (60J65 60J80 92D15)},
mrnumber = {MR2100386 (2005h:60259)},
mrreviewer = {Laurent Mazliak},
note = {arxiv:math/0503577},
number = 4,
pages = {2120--2148},
timestamp = {2012-04-23T01:33:10.000+0200},
title = {Asymptotic genealogy of a critical branching process},
url = {http://www.projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.aoap/1099674091&page=record},
volume = 14,
year = 2004
}