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A NOTE ON THE ASYMPTOTIC BEHAVIOR OF THE HEIGHT FOR A BIRTH-AND-DEATH PROCESS

Published online by Cambridge University Press:  08 July 2020

Feng Wang Open the ORCID record for Feng Wang [Opens in a new window] ,
Xian-Yuan Wu  and
Rui Zhu
Feng Wang
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing100048, China E-mail: wangf@mail.cnu.edu.cn; wuxy@cnu.edu.cn; lmozi999@163.com
Xian-Yuan Wu
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing100048, China E-mail: wangf@mail.cnu.edu.cn; wuxy@cnu.edu.cn; lmozi999@163.com
Rui Zhu
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing100048, China E-mail: wangf@mail.cnu.edu.cn; wuxy@cnu.edu.cn; lmozi999@163.com
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Abstract

Recently, the asymptotic mean value of the height for a birth-and-death process is given in Videla [Videla, L.A. (2020)]. We consider the asymptotic variance of the height in the case when the number of states tends to infinity. Further, we prove that the heights exhibit a cutoff phenomenon and that the normalized height converges to a degenerate distribution.

Keywords

birth-and-death processcutoffheight function distribution
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 41 - 48
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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