Size-biased branching population measures and the multi-type $x\log x$ condition

Peter Olofsson

doi:10.3150/09-BEJ211

Size-biased branching population measures and the multi-type $x\log x$ condition

Statistics Theory 2010-01-14 v1 Statistics Theory

Authors: Peter Olofsson

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Abstract

We investigate the $x\log x$ condition for a general (Crump--Mode--Jagers) multi-type branching process with a general type space by constructing a size-biased population measure that relates to the ordinary population measure via an intrinsic martingale $W_t$ . Sufficiency of the $x\log x$ condition for a non-degenerate limit of $W_t$ is proved and conditions for necessity are investigated.

Keywords

branching processes size-biased measure x log x condition martingale Crump-Mode-Jagers process multi-type

Cite

@article{arxiv.1001.2138,
  title  = {Size-biased branching population measures and the multi-type $x\log x$ condition},
  author = {Peter Olofsson},
  journal= {arXiv preprint arXiv:1001.2138},
  year   = {2010}
}

Comments

Published in at http://dx.doi.org/10.3150/09-BEJ211 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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