报告题目：Extinction Probabilities and Asymptotic Behaviour of Interacting Branching Collision Processes

报告人：Anyue Chen University of Liverpool & South University of Science and Technology of China

报告时间：1月5日 16:00 管理科研楼1518

摘要：In this talk, I’ll address some important topics, particularly the extinction properties and their asymptotic behaviour of the Interacting Branching Collision Process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process (MBP) and a collision branching process (CBP). After establishing some elegant necessary and sufficient conditions for existence and uniqueness of IBCP, the explicit expressions are then obtained for the extinction probabilities for the regular, critical-explosive and super-explosive cases. The subtle sub-explosive case will also be addressed. The associated expected hitting times are also investigated and revealed. Moreover, considering some of these exact explicit expressions are very complicated and thus we turn to investigate the asymptotic behaviour of these extremely complicated and divergent expressions for extinction probabilities. Surprisingly, we are able to show that the asymptotic behaviour follows an elegant and homogenous power law with an index quantity.  We further show that this interesting and important index quantity takes a very simple and uniform form which could be interpreted as the “spectrum, ranging from minus infinity to positive infinity, of the interaction between the two components of the IBCP.

主办单位：中国科学技术大学数学科学学院    

中科院吴文俊数学重点实验室 

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