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June 2015 Exponential growth of bifurcating processes with ancestral dependence
Sana Louhichi, Bernard Ycart
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Adv. in Appl. Probab. 47(2): 545-564 (June 2015). DOI: 10.1239/aap/1435236987

Abstract

Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes are considered here, in particular bifurcating Markov chains. Under the hypotheses of stationarity and multiplicative ergodicity, the corresponding branching process is proved to have the same type of asymptotics as its classic counterpart in the independent and identically distributed supercritical case: the cell population grows exponentially, the growth rate being related to the exponent of multiplicative ergodicity, in a similar way as to the Laplace transform of lifetimes in the i.i.d. case. An identifiable model for which the multiplicative ergodicity coefficients and the growth rate can be explicitly computed is proposed.

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Sana Louhichi. Bernard Ycart. "Exponential growth of bifurcating processes with ancestral dependence." Adv. in Appl. Probab. 47 (2) 545 - 564, June 2015. https://doi.org/10.1239/aap/1435236987

Information

Published: June 2015
First available in Project Euclid: 25 June 2015

zbMATH: 1318.60088
MathSciNet: MR3360389
Digital Object Identifier: 10.1239/aap/1435236987

Subjects:
Primary: 60J85
Secondary: 92D25

Keywords: bifurcating Markov chain , branching process , cell kinetics , multiplicative ergodicity

Rights: Copyright © 2015 Applied Probability Trust

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Vol.47 • No. 2 • June 2015
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