隐马尔可夫链熵率的分析性
概率论
2007-07-13 v4 信息论
math.IT
摘要
我们证明在温和的正性假设下，隐马尔可夫链的熵率作为底层马尔可夫链参数的函数是解析变化的。我们陈述了确定解析域的一般原理。并给出一个例子来估计熵率的收敛半径。然后我们说明正性假设可以放宽，并给出满足放宽条件的例子。我们更详细地研究了一类特殊的隐马尔可夫链：具有无歧义符号的二元隐马尔可夫链，并给出了此类情况下熵率解析性的充要条件。最后，我们证明在正性假设下隐马尔可夫链本身在强意义下作为底层马尔可夫链参数的函数是解析变化的。
引用
@article{arxiv.math/0507235,
title = {Analyticity of Entropy Rate of Hidden Markov Chains},
author = {Guangyue Han and Brian Marcus},
journal= {arXiv preprint arXiv:math/0507235},
year = {2007}
}
备注
The title has been changed. The new main theorem now combines the old main theorem and the remark following the old main theorem. A new section is added as an introduction to complex analysis. General principle and an example to determine the domain of analyticity of entropy rate have been added. Relaxed conditions for analyticity of entropy rate and the corresponding examples are added. The section about binary markov chain corrupted by binary symmetric noise is taken out (to be part of another paper)