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...

Limiting distributions for the spent and residual life times in a superposition of independent renewal processes are obtained in the case when the interarrival times belong to domains of attraction of stable laws.

Stem and precursor cells play a critical role in tissue development, maintenance, and repair throughout the life. Often, experimental limitations prevent direct observation of the stem cell compartment, thereby posing substantial challenges to the analysis of such cellular systems. Two-type...