Unified characteristic numbers and solutions of equations for birth and death processes with barriers

作者：Yang, Xiang-qun^*; Wang, He-song

来源：Acta Mathematicae Applicatae Sinica-English Series, 2010, 26(3): 443-454.

DOI：10.1007/s10255-010-0009-y

• birth and death process with barrier
• reflection and absorption
• leaping reflection and quasi-reflection
• characteristic numbers
• solutions of equations

The state 0 of a birth and death process with state space E = {0, 1, 2, aEuro broken vertical bar } 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.

• 出版日期2010-7
• 单位长沙理工大学; 湖南师范大学