A note on the asymptotic behavior of the height for a birth-and-death process

Feng Wang; Xian-Yuan Wu; Rui Zhu

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arXiv · 1912.07422

A note on the asymptotic behavior of the height for a birth-and-death process

Feng Wang·Xian-Yuan Wu·Rui Zhu

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Abstract

This paper focuses on the asymptotic behaviors of the {\it height} for a birth-and-death process which related to a mean-field model \cite{FFS}(or the Anick-Mitra-Sondhi model \cite{DDM}). Recently, the asymptotic mean value of the height for the model is given in \cite{LAV}. In this paper, first, the asymptotic variance of the height is given, and as a consequence, a weak Law of Large Number for the height is obtained. Second, the centered and normalized height is proved to converge in distribution to a degenerate distribution, this indicates that the desired Central Limit Theorem fails.

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Feng Wang, Xian-Yuan Wu, Rui Zhu. 2019-12-16. A note on the asymptotic behavior of the height for a birth-and-death process. https://arxiv.org/abs/1912.07422

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