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2 results

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

  • Part of
  • Christine Reder
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 4 / September 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 1007-1030
    Print publication:
    September 2003

  • 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.