中文摘要：

在许多应用领域,高阶Markov模型正成为研究长期相关性的重要工具之一.为了克服现有高阶Markov模型不能从事动态规律研究这一缺点,讨论从初始状态到任意给定期状态转移概率的表示方法,方便动态数据分析.另外,也给出平稳分布的表达式,为稳态研究提供工具.由于研究结果与一阶Markov链的情况类似,极大地降低了高阶Markov链应用于各领域时的难度.

英文摘要：

In many applications, the high-order Markov model is an important tool to study the long-term correlation. In order to overcome the shortcomings that the existing model for high-order Markov can not engage dynamics,the representation of transition prob- ability from initial state to any state is discussed, it facilitates the study of dynamic data. And the expression of stationary distribution is given too, which provide a tool for steady-state study. Since the result is similar to first order Markov chain, the difficulty is greatly reduced while applying higher-order Markov chain to various fields.