Author(s): Sun Yinghua, Yang Weiguo
Pages: 380-386
Year: 2015 Issue:  4
Journal: Pure and Applied Mathematics
Keyword:  second-order hidden Markov model; observation chain; hidden chain;
Abstract: 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.