A note on the asymptotic behavior of the height for a birth-and-death process
Probability
2019-12-17 v1
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.
Keywords
Cite
@article{arxiv.1912.07422,
title = {A note on the asymptotic behavior of the height for a birth-and-death process},
author = {Feng Wang and Xian-Yuan Wu and Rui Zhu},
journal= {arXiv preprint arXiv:1912.07422},
year = {2019}
}
Comments
11 pages