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 ...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 th, processes are also investigated and resolved.展开更多
A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction tim...A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos 11371374 and 11571372)Research Fund for the Doctoral Program of Higher Education of China (Grant No 20110162110060)
文摘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 th, processes are also investigated and resolved.
基金supported by National Natural Science Foundation of China (Grant No.10771216)Research Grants Council of Hong Kong (Grant No.HKU 7010/06P)Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministry of China (Grant No.[2007]1108)
文摘A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.
