Critical randomly indexed branching processes

Georgi K. Mitov, Kosto V. Mitov and Nikolay M. Yanev

Statistics & Probability Letters, 2009, vol. 79, issue 13, 1512-1521

Abstract: Bienaymé-Galton-Watson branching processes subordinated to a continuous time random index are considered. The branching processes are assumed to be critical with finite or infinite offspring variance. The indexing process is assumed to be a renewal one with finite or infinite mean of the interarrival times. Under these conditions we prove the asymptotic formulas for the first two moments and for the probability of non-extinction. We also obtain proper limiting distributions under suitable normalization.

Date: 2009
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