Advances in Applied Probability

Exponential growth of bifurcating processes with ancestral dependence

Sana Louhichi and Bernard Ycart

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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.

Article information

Adv. in Appl. Probab., Volume 47, Number 2 (2015), 545-564.

First available in Project Euclid: 25 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J85: Applications of branching processes [See also 92Dxx]
Secondary: 92D25: Population dynamics (general)

Branching process bifurcating Markov chain multiplicative ergodicity cell kinetics


Louhichi, Sana; Ycart, Bernard. Exponential growth of bifurcating processes with ancestral dependence. Adv. in Appl. Probab. 47 (2015), no. 2, 545--564. doi:10.1239/aap/1435236987.

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