A Two-Type Bellman–Harris Process Initiated by a Large Number of Particles
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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 −β, β∈(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 0≤t<∞ splits into several regions whose ranges depend on β and the ratio N/t within each of which the process at time t exhibits asymptotics (as N,t→∞) which is different from those in the other regions.
KeywordsEvolutionary stages Two-type critical Bellman–Harris process Regular variation Renewal theory
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