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Existence,uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection

science china Mathematics 2008年第7期51卷 1266-1286页

作者： li junping1 & chen anyue2,3 1 school of mathematical science and computing technology,central south university,changsha410075,china 2 Department of mathematical sciences,The university of liverpool,liverpool,L69 7ZL,UK 3 Department of Statistics and Actuarial science,university of Hong Kong,Pokfulam Road,Hong Kong,china 1. school of mathematical science and computing technology Central South University Changsha 410075 China 2. Department of mathematical sciences The University of Liverpool Liverpool L69 7ZL UK 3. Department of Statistics and Actuarial science University of Hong Kong Pokfulam Road Hong Kong China

We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous *** existence criterion of the process is firstly *** prove that if the sum of the resurrection rates is finite,then there does not exist any *** existence criterion is then established when the sum of the resurrection rates is *** equivalent criteria,possessing the advantage of being easily checked,are obtained for the latter *** uniqueness criterion for such process is also *** prove that although there exist infinitely many of them,there always exists a unique honest process for a given *** unique honest process is then *** ergodicity property of this honest process is analysed in *** prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.

关键词： Markov branching process immigration resurrection recurrence ergodicity 60J27 60J80

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Generalized Markov interacting branching processes

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science china Mathematics 2018年第3期61卷 545-562页

作者： junping li anyue chen school of Mathematics and Statistics Central South University Department of Mathematics Southern University of Science and Technology Department of mathematical sciences The University of Liverpool

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 *** mean explosion time and the total mean life time of th, processes are also investigated and resolved.

关键词： generalized Markov interacting branching process regularity extinction probability mean extinction time mean explosive time total mean life time

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General collision branching processes with two parameters

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science china Mathematics 2009年第7期52卷 1546-1568页

作者： chen anyue li junping Department of mathematical sciences the University of LiverpoolLiverpoolL69 7ZLUK Department of Statistics and Actuarial science University of Hong KongPokfulam RoadHong Kong school of mathematical science and computing technology Central South UniversityChangsha 410075China

A new class of branching models,the general collision branching processes with two parameters,is considered in this *** such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing *** and uniqueness criteria are firstly *** expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction *** explosion behavior of these models is investigated and an explicit expression for mean explosion time is *** mean global holding time is also *** is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.

关键词： Markov branching process general collision branching process uniqueness extinction probabilities mean extinction time mean explosion time 60J27 60J80

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