Relative frequencies in multitype branching processes

Details Relative frequencies in multitype branching processes Relative frequencies in multitype branching processes

2009-02-27

arxiv.org/abs/0902.4773v1

Annals of Applied Probability 2009, Vol. 19, No. 1, 1-14

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP539

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell biology. Specifically, the reported limiting results are of advantage in cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement. Relevant statistical applications are discussed in the context of asymptotic maximum likelihood inference for multitype branching processes.

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