Some Strong Limit Theorems Of Hidden Nonhomogeneous Markov Model And Its Strong Markov Properties

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 theory research of hidden Markov models are not perfect .In practice, it happens that the state chain is a nonhomogeneous.hidden Markov models are difficult to manage,we also need set up hidden nonhomogeneous Markov models to solve some problems , such as Dynamic graphical models, climate forecast. However, theory research of hidden nonhomogeneous Markov models are basically blankness. It is important meaningful to study the hidden nonhomogeneous Markov models.The purpose of this thesis is to study the strong limit theorem of Hidden nonhomogeneous Markov models and its transforms limit theorems. In this paper, firstly, the author introduces some knowledge about hidden Markov models including the simple definition and the application of hidden Markov models , the advantages the equivalent definition and some properties, we introduce the notion of strong Markov property of hidden Markov model ,some strong Markov properties are obtaine-d,etc. Secondly, we obtain some strong law of large numbers for functionals of hidden nonhomogeneous Markov model by means of the martingable theory and the coefficient. It is also easy to get some conclusion we have done. In the end, we study the limit theorems on the transformation for ergodic hidden nonhomogeneous Markov models by means of martingale limit theory. As a special case,the idea of random transformation of gambling system is expended to the hidden nonhomogenous models. As results, some strong limit theorems and random equitable ratios for their random selection are are obtained.