The Classification of States for Markov Chain in Random Environments and m-irreducible

First of all,we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible,the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible,for any two states in X ,they have the same period.     

The convergence of statistically self-similar sets and the upper bound and lower bound of Hausdorff measure

We constructed a class of self-similar sets and proved the convergence in this paper. Besides these, the upper bound and lower bound of Hausdorff measures of them were given too. Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China Hu Dihe: born in May 1935, Professor     

Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q-process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q-processes in random environments.     

The classification of statistically recursive sets

The main aim of this paper is to make a classification of random setsK _m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK _m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification. Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China Hu Dihe: born in May 1935, Professor     

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.     

The construction of statistically recursive sets

We have constructed a class of random sets by statistical contraction operators in this paper. When the probability space is some special product space and the statistical contraction operators are affine or similar, these statistically recursive sets are investigated by many authors. It will be very convenient for us to study their distributions and dimensions and measures using our model in this paper. Supported by the National Natural Science Foundation and the Doctoral Progamme Foundation of China Hu Dihe: born in 1935, Professor     

The construction of statistically self-similar measures

We have studied statistically self-similar measures together with statistically self-similar sets in this paper. A special kind of statistically self-similar measures has been constructed and a class of statistically self-similar sets as well. Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China Hu Dihe: born in May 1935, Professor     

The Classificat,on of States for Markov Chain in Random Environments and m-irreducible

First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.