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Transient behaviour of a Galton–Watson process with a large number of types

  • Christine Reder (a1)
Abstract

Modelling the distribution of mutations of mitochondrial DNA in exponentially growing cell cultures leads to the study of a multitype Galton–Watson process during its transient phase. The number of types corresponds to the number of mtDNA per cell and may be considered as large. By taking advantage of this fact we prove that the stochastic process is deterministic-like on the set of nonextinction. On this set almost all trajectories are well approximated by the unique solution of a partial differential problem. This result allows also the comparison of trajectories corresponding to different modelling assumptions, for instance different values of the number of types.

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Corresponding author
Postal address: Institut de Mathématiques, Université de Bordeaux 1, 351 Cours de la Libération, F-33405 Talence Cedex, France. Email address: christine.reder@math.u-bordeaux.fr
References
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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