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

作者：Vatutin Vladimir; Iksanov Alexander^*; Topchii Valentin

来源：Acta Applicandae Mathematicae, 2015, 138(1): 279-312.

DOI：10.1007/s10440-014-9966-0

• Evolutionary stages
• Two-type critical Bellman-Harris process
• Regular variation
• Renewal theory

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.

• 出版日期2015-8