非齐次马氏链缺失数据一元函数的强大数定律

Strong Law of Large Numbers for Functions of One Variable of MissingData of Nonhomogeneous Markov Chains

为研究非齐次马氏链缺失数据一元函数的强大数定律.首先给出了非齐次马氏链缺失数据的一个定义,由这个定义说明作为非齐次马氏链的子列,缺失数据显然也具有马氏性.在前人研究马氏链收敛性的基础上,通过鞅差收敛定理给出非齐次马氏链缺失数据一元函数平均极限定理,再由这个极限定理,给出了非齐次马氏链缺失数据的一元函数满足强大数定律的一个充分条件和几个推论。

The strong law of large numbers for functions of one variable of missing data of nonhomogeneous Markov chains is studied. Firstly a definition of the missing data of nonhomogeneous Markov chains is given, from this definition that missing data obviously has Markov properties when it is a subsequence of nonhomogeneous Markov chains. Under the basis of other ones＇ study of convergence of Markov chains, a limit theorem for the averages of the functions of one variable of the missing data of nonhomogeneous Markov chains by using the convergence theorem for martingale difference sequences is given. Then, the of missing data of nonhomogeneous Markov chains by using are given. strong law of large numbers for functions of one variable the limit theorem is provde, finally, several corollaries