A note on the asymptotic behavior of the height for a birth-and-death process
PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES(2022)
摘要
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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关键词
birth-and-death process,cutoff,height function distribution
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