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On the convergence of supercritical general C-M-J branching processes

by: Olle Nerman

In: Probability Theory and Related Fields, Vol. 57, Nr. 3 (September 1981) , p. 365--395.

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URL:	http://dx.doi.org/10.1007/BF00534830

Convergence in probability of Malthus normed supercritical general branching processes i.e. Crump-Mode-Jagers branching processes counted with a general characteristic are established, provided the latter satisfies mild regularity conditions. If the Laplace transform of the reproduction point process evaluated in the Malthusian parameter has a finite ‘x log x-moment’ convergence in probability of the empirical age distribution and more generally of the ratio of two differently counted versions of the process also follow. ER -

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SpringerLink - Journal Article

BibTeX record

@article{olle1981convergence,
  abstract = {Convergence in probability of Malthus normed supercritical general branching processes (i.e. Crump-Mode-Jagers branching processes) counted with a general characteristic are established, provided the latter satisfies mild regularity conditions. If the Laplace transform of the reproduction point process evaluated in the Malthusian parameter has a finite ‘x log x-moment’ convergence in probability of the empirical age distribution and more generally of the ratio of two differently counted versions of the process also follow.
ER  -},
  added-at = {2009-07-03T04:33:39.000+0200},
  author = {Nerman, Olle},
  biburl = {http://www.bibsonomy.org/bibtex/25188727be38bd3bc0cca61f86acfaa88/ebo},
  description = {SpringerLink - Journal Article},
  interhash = {3272da18b777448bd2f4dc3447e24edc},
  intrahash = {5188727be38bd3bc0cca61f86acfaa88},
  journal = {Probability Theory and Related Fields},
  keywords = {branching imported stochastic},
  month = {#sep#},
  number = 3,
  pages = {365--395},
  timestamp = {2009-07-03T04:33:39.000+0200},
  title = {On the convergence of supercritical general (C-M-J) branching processes},
  url = {http://dx.doi.org/10.1007/BF00534830},
  volume = 57,
  year = 1981
}

Endnote record