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| The state 0 of a birth and death process with state space E={0,1,2,…} is a barrier which can be divided 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 respectively .In this paper the 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 is a basic work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier. |
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| Keywords:birth and death process with barrier , reflection barrier and absorption barrier , leaping reflection barrier and quasi-reflection barrier , unified characteristic numbers , solutions of equation |
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