caa a22 4500 606166033 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10440-014-9966-0 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9966-0 A Two-Type Bellman-Harris Process Initiated by a Large Number of Particles [Elektronische Daten] [Vladimir Vatutin, Alexander Iksanov, Valentin Topchii] 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. Springer Science+Business Media Dordrecht, 2014 Evolutionary stages nationallicence Two-type critical Bellman-Harris process nationallicence Regular variation nationallicence Renewal theory nationallicence Vatutin Vladimir Steklov Mathematical institute RAS, Gubkin str. 8, 119991, Moscow, Russia aut Iksanov Alexander Faculty of Cybernetics, National Taras Shevchenko University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine aut Topchii Valentin Sobolev Institute of Mathematics SB RAS, 630090, Novosibirsk, Russia aut Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 279-312 0167-8019 138:1<279 2015 138 10440 https://doi.org/10.1007/s10440-014-9966-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9966-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vatutin Vladimir Steklov Mathematical institute RAS, Gubkin str. 8, 119991, Moscow, Russia aut NATIONALLICENCE 700 1- Iksanov Alexander Faculty of Cybernetics, National Taras Shevchenko University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Topchii Valentin Sobolev Institute of Mathematics SB RAS, 630090, Novosibirsk, Russia aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 279-312 0167-8019 138:1<279 2015 138 10440