Generalized Markov interacting branching processes
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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 mean explosion time and the total mean life time of the processes are also investigated and resolved.
Keywordsgeneralized Markov interacting branching process regularity extinction probability mean extinction time mean explosive time total mean life time
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11371374 and 11571372) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110162110060).