Mixing Property Of Hidden Nonhomogeneous Markov Models

Hidden Markov models have during the last decade become widespread for modeling sequences of weakly dependent random variables,with applications in areas such as speech processing,neurophysiology and biology.Hidden Markov models are widely applied,but its theorem foundation are not perfect,and we should set up Hidden Markov models in the practiced application such as Dynamic graphical models,climate forecast.Because Hidden Markov models are difficult to manage,theory research of Hidden nonhomogeneous Markov models are basically blankness.It is important meaning to study the Hidden nonhomogeneous Markov models.The purpose of this is to study the mixing property of hidden nonhomogeneous Markov models.In this paper,firstly,it introduces some knowledge about Hidden Markov models.Secondly,we study the mixing property of first order hidden nonhomogeneous Markov models,the sufficient condition for nonhomogeneous Markov chains to meet this kind of mixing property is given and proved,and the results about nonhomogeneous Markov chains are extended to the hidden nonhomogeneous Markov models.In the end,we study the mixing property of m th order hidden nonhomogeneous Markov models,the definition of the mixing property of m th order nonhomogeneous Markov chains is given,and the sufficient condition for m th order nonhomogeneous Markov chains to meet this kind of mixing property is proved by using the definition and lemma,and then the results about nonhomogeneous Markov chains are extended to the hidden nonhomogeneous Markov models,which provides some theoretical bases for further studying multi-order hidden Markov models and some practical problems such as modeling sequences of weakly dependent random variables,speech processing, neurophysiology and biology.