The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 1 (2009), 1-14.
Relative frequencies in multitype branching processes
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.
Ann. Appl. Probab., Volume 19, Number 1 (2009), 1-14.
First available in Project Euclid: 20 February 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx]
Secondary: 62P10: Applications to biology and medical sciences 92D25: Population dynamics (general)
Yakovlev, Andrei Y.; Yanev, Nikolay M. Relative frequencies in multitype branching processes. Ann. Appl. Probab. 19 (2009), no. 1, 1--14. doi:10.1214/08-AAP539. https://projecteuclid.org/euclid.aoap/1235140330