Size-Biased Branching Population Measures and the Multi-Type x Log x Condition
نویسنده
چکیده
We investigate the x log x condition for a general (Crump–Mode– Jagers) multi-type branching process with arbitrary type space by constructing a size-biased population measure that relates to the ordinary population measure via the intrinsic martingale Wt. Sufficiency of the x log x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated. GENERAL BRANCHING PROCESS; XLOGX CONDITION; IMMIGRATION; SIZE-BIASED MEASURE AMS 2000 SUBJECT CLASSIFICATION: PRIMARY 60J80
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