AI 中文总结
研究正则高阶马尔可夫链，解释其极限概率分布为边际平稳分布，证明其性质并建立收敛速率结果，还引入边际混合时间，扩展了一阶马尔可夫链混合时间概念到高阶链。
AI 中文摘要
对于正则高阶马尔可夫链，其约化一阶链可能不可约，此时没有唯一平稳分布。但正则高阶链当前状态的概率分布会收敛到唯一极限概率分布。本文将此极限分布解释为边际平稳分布并证明其性质，建立了这种收敛的速率结果，还引入了两种边际混合时间，将一阶马尔可夫链的混合时间概念扩展到高阶链。
英文摘要
For a regular higher order Markov chain, its reduced first order chain may be reducible. When the reduced first order chain is reducible, it does not have a unique stationary distribution. However, it has been shown that the probability distribution of the current state of a regular higher order chain converges to a unique limiting probability distribution. In this paper, we interpret this limiting distribution as a marginal stationary distribution and prove some properties of marginal stationary distributions. We then establish some convergence rate results for such type of convergence. Finally, we introduce two types of marginal mixing times, which extend the notions of mixing times for first order Markov chains to higher order chains.
Comments19 pages
