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1 results

  • Extinction of non-homogeneous Galton-Watson processes

  • Miloslav Jirina
  • Journal:
    Journal of Applied Probability / Volume 13 / Issue 1 / March 1976
    Published online by Cambridge University Press:
    14 July 2016, pp. 132-137
    Print publication:
    March 1976

  • In the paper the problem of the extinction of non-homogeneous Galton-Watson processes with one type of particle is studied. It is proved that the process becomes extinct if the expectations of the process do not converge to a limit (finite or infinite). If the expectations have a finite limit, then simple necessary and sufficient conditions for the extinction are proved. The general case remains open; however two more sufficient conditions which are also necessary under some restrictions are given.