We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial ...We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11071021)
文摘We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.
