A Two-Type Bellman-Harris Process Initiated by a Large Number of Particles

We investigate a two-type critical Bellman-Harris branching process with the following properties: the tail of the life-length distribution of the first type particles is of order o(t (-2)); the tail of the life-length distribution of the second type particles is regularly varying at infinity with index -beta, beta a(0,1]; at time t=0 the process starts with a large number N of the second type particles and no particles of the first type. It is shown that the time axis 0a parts per thousand currency signt < a splits into several regions whose ranges depend on beta and the ratio N/t within each of which the process at time t exhibits asymptotics (as N,t -> a) which is different from those in the other regions.