Uniqueness,Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction |
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| Authors: | Anyue Chen Phil Pollett Junping Li Hanjun Zhang |
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| Institution: | 1.Department of Mathematical Sciences,The University of Liverpool,Liverpool,UK;2.Department of Statistics and Actuarial Science,University of Hong Kong,Pokfulam,Hong Kong;3.Department of Mathematics,University of Queensland,Brisbane,Australia;4.School of Mathematical Sciences and Computing Technology,Central South University,Changsha,China;5.School of Mathematics and Computing Science,Xiangtan University,Xiangtan,China |
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| Abstract: | We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes
with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process
is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case
the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities,
the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression
for mean explosion time is established. |
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