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On the Asymptotic Behaviour of the Population Number
Author(s) -
Karev G. P.,
Treskov S. A.
Publication year - 1978
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710200208
Subject(s) - mathematics , generalization , population , branching (polymer chemistry) , basis (linear algebra) , convergence (economics) , convergence of random variables , random variable , statistics , combinatorics , demography , mathematical analysis , materials science , sociology , economics , composite material , economic growth , geometry
We consider the stochastic model of an asexual population in which the number of couples formed in some generation is random variable depending on the number of individuals in that generation only. The conditions of convergence were obtained almost everywhere and in mean square of the normalized number of individuals in the n ‐th generation. These results may be considered as the generalization of some known statements about the models constructed on the basis of the branching processses theory.