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HITTING TIME DISTRIBUTIONS FOR BIRTH–DEATH PROCESSES WITH BILATERAL ABSORBING BOUNDARIES

Published online by Cambridge University Press:  13 September 2016

Yong-Hua Mao  and
Chi Zhang
Yong-Hua Mao
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
Chi Zhang
Affiliation:
College of Mathematical Sciences, College of Information Science and Engineering Ocean University of China, Qingdao 266100, People's Republic of China E-mail: zhangchi@ouc.edu.cn
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Abstract

For the birth–death process on a finite state space with bilateral boundaries, we give a simpler derivation of the hitting time distributions by h-transform and φ-transform. These transforms can then be used to construct a quick derivation of the hitting time distributions of the minimal birth–death process on a denumerable state space with exit/regular boundaries.

Keywords

stochastic modelling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 3 , July 2017 , pp. 345 - 356
Copyright
Copyright © Cambridge University Press 2016 

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