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A NOTE ON THE ASYMPTOTIC BEHAVIOR OF THE HEIGHT FOR A BIRTH-AND-DEATH PROCESS
Feng Wang, Xian-Yuan Wu, Rui Zhu
Journal:

Probability in the Engineering and Informational Sciences / Volume 36 / Issue 1 / January 2022

Published online by Cambridge University Press:

08 July 2020, pp. 41-48
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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.

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