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.
Citation
Peter Olofsson. "Size-biased branching population measures and the multi-type $x \log x$ condition." Bernoulli 15 (4) 1287 - 1304, November 2009. https://doi.org/10.3150/09-BEJ211
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