Relation Of Two Order Markov Chains And Some Class Of Finite Markov Fields With Neighbor Gibbs Fields

Markov chain is a mathematic model describing practical problems,it has got rich progress in many areas such as economics,biology,stochastic service system,computer science. The research about limit theorems and ergodic properties has been researching in recent years.The definition of mth-order nonhomogeneous Markov chain is an extension of the definition of Markov chain.Mth-order Markov information source is an important information source .So the research about the theory of mth-order Markov chain is very important. Thirty years ago, when random fields came into being. It 's a subject of intersection of Probability and Statistical Physics.The purpose of this thesis is to study the relation of the mth-order Markov chains and some class of fields.The main result is to study the relation of the two order Markov chains and some class of finite Markov fields and neighbor Gibbs fields. In this paper, firstly , the author defines the two order two-sided Markov property of and proves the two order Markov chains {X_n,0≤n≤N} satisfies the two oder two-sided Markovproperty.Secondly,a neighbor system d is defined ,we not only prove the two order Markov chains {X_n,0≤n≤N} is some class of finite Markovfields but also give the expression of local characteristics. Finally, using the equivalence of finite Markov and neighbor Gibbs fields,we prove the two order Markov chains {X_n,0≤n≤N} is some class of Gibbs fields and give the expression of canonical potential.