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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 School of Mathematical Science and Computing Technology Central South University Changsha China Department of Mathematical Sciences The University of Liverpool Liverpool UK Department of Statistics and Actuarial Science University of Hong Kong 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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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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