二阶离散隐马尔科夫模型的严格定义及等价性质

The strict definition of second-order discrete hidden Markov model and its equivalent nature

隐马氏模型作为一种具有双重随机过程的统计模型,具有可靠的概率统计理论基础和强有力的数学结构,已被广泛应用于语音识别、生物序列分析、金融数据分析等领域.由于传统的一阶隐马氏模型无法表示更远状态距离间的依赖关系,就可能会忽略很多有用的统计特征,故有人提出二阶隐马氏模型的概念,但此概念并不严格.本文给出二阶离散隐马尔科夫模型的严格定义,并研究了二阶离散隐马尔科夫模型的两个等价性质.

Hidden Markov model, as a statistical model of doubly stochastic process, has a reliable theoretical foundation in probability and statistics and strong mathematical structure. It has been widely used in speech recognition, biological sequence analysis, financial data analysis, etc. As the conventional first-order hidden Markov model can not express the dependency relationship between the further distance, many useful statistical characteristic were ignored in many works. Therefore, the concept of second-order hidden Markov model was put forward, but this concept is not strict. In this paper, we give the strict definition of second-order discrete hidden Markov model and study two equivalent properties of the second-order discrete hidden Markov model.