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中文摘要：
设{Xn,n≥0}是在有限状态空间中取值的随机变量序列,设它在概率测度P下是一渐近循环马氏链,在概率测度Q下是一齐次马氏链.散度率在熵、相对熵与互信息中起重要作用.研究了渐近循环马氏链的散度率.利用渐近循环马氏链的渐近均分割性以及随机变量序列的一致可积性,得到了渐近循环马氏链关于齐次马氏链的散度率,并推广了一个已知结果.
英文摘要：
{Xn,n≥0}was assumed to be a sequence of random variables taken in finite alphabet set,and to be an asymptotic circular Markov chain and a homogeneous Markov chain under a probability measure P and a probability measure Q,respectively.Divergence rate plays an important role for entropy,relative entropy and mutual information.The divergence rate of asymptotic circular Markov chains was investigated.The divergence rate for asymptotic circular Markov chains related to homogeneous Markov chains was achieved by AEP for asymptotic circular Markov chains and uniform integrability of random variable sequences.As corollary,a known result was generalized.
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