Unified representation of formulas for single birth processes  

作　　者：Mu-Fa CHEN Yuhui ZHANG 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics andComplex Systems, Ministry of Education, Beijing 100875, China

出　　处：《Frontiers of Mathematics in China》2014年第4期761-796,共36页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11131003）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, the ＂985＂ project from the Ministry of Education in China, the Fundamental Research Funds for the Central Universities, and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

摘　　要：Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.

关 键 词：Single birth process Poisson equation UNIQUENESS recurrence ergodicity moments of return time 

分 类 号：O211.62[理学—概率论与数理统计] O241.82[理学—数学]