The purpose of this paper is to establish a class of strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results.
In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class o...In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.展开更多
Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,T...Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.展开更多
基金supported by National Natural Science foundation of China(11071104)
文摘The purpose of this paper is to establish a class of strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results.
基金supported by the National Natural Science Foundation of China(Nos.11571142,11971197,11601191)。
文摘In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.
文摘Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.
