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

2009/11/01 by Peter Olofsson · 2 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.ST #stat.TH

paper · pdf · doi:10.3150/09-bej211

published as Bernoulli 2009, Vol. 15, No. 4, 1287-1304 · 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)

openalex publication_date 2009/11/01 · arxiv created 2010/01/13 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

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