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Relative Frequencies in Multitype Branching Processes

Andrei Y. Yakovlev and Nikolay M. Yanev
The Annals of Applied Probability
Vol. 19, No. 1 (Feb., 2009), pp. 1-14
Stable URL: http://www.jstor.org/stable/30243569
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Relative Frequencies in Multitype Branching Processes
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Abstract

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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