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4. Generalized Markov interacting branching processes

Author

Chen Anyue and Li Junping

Subjects
Extinction, Markov chain, Extinction probability, General Mathematics, 010102 general mathematics, Conditional expectation, 01 natural sciences, Combinatorics, Branching (linguistics), 010104 statistics & probability, Extinction time, Uniqueness, Statistical physics, 0101 mathematics, Mathematics, Branching process
Abstract

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness. Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed. The meanexplosion time and the total mean life time of the processes are also investigated and resolved.

Published
2017

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