Unified Characteristic Numbers and Solutions of Equations for Birth and Death Processes with Barriers  

作　　者：Xiang-qun Yang He-song Wang 

机构地区：[1]College of Mathematics and Computer Science, Hunan Normal University. Changsha 410081, China [2]College of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha410076, China

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第3期443-454,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10571051 and 10871064 );the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20040542006);the Key Labor. of Coput.Stoch.Math.Univ. of Hunan (No. 09K026)

摘　　要：The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds： reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds： reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.

关 键 词：birth and death process with barrier reflection and absorption leaping reflection andquasi-reflection characteristic numbers solutions of equations 

分 类 号：O153.3[理学—数学] O175.1[理学—基础数学]