Critical randomly indexed branching processes

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

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.

Mots clés: 60J80; 60F05

Georgi K. Mitov, Kosto V. Mitov, Nikolay M. Yanev. Critical randomly indexed branching processes. Statistics and Probability Letters, 2009, 79 (13), pp.1512. ⟨10.1016/j.spl.2009.03.010⟩. ⟨hal-00542571⟩