马氏过程的极限理论有着重要的理论意义和很强的应用背景，是概率极限理论的热点研究内容之一，本项目主要研究了马氏过程中各种混合随机变量的极限理论，获得的主要结果有：NA随机变量序列的几乎处处收敛性和特征指数属于（0，2）和2的Chover型重对数率，两两NQD随机变量序列的Marcinkiewicz型和Jamison型强大数律，线性模型ND随机误差等的M估计在较弱矩条件下的强相合性，混合序列部分和的几乎处处收敛的一些等价条件和Chover型k重对数率，加权乘积和的强极限定理，阵列行和的若干极限定理，广义生-灭最小Q过程的常返、遍历性等等，以上这些成果大部分都达到了独立情形的理想结果，已在SCI期刊源发表或录用论文7篇，在核心刊物发表论文19篇；另外，还获得了平稳过程的部分和以及部分和的乘积的几乎处处中心极限定理，已向SCI期刊投稿2篇，正在审稿之中。这些研究成果对马氏过程理论的发展有着一定的理论和实际意义。.本项目培养研究生22人，其中已毕业12人，这些研究生都参与了本项目的研究工作，初步具备了独立做研究的能力，取得了不少的研究成果，已发表或录用的论文29篇。

Limit theory of the Markov process has important theoretical significance and strong application background. It is the one of the hot research of probability limit theory. The project mainly studied limit theory of the Markov process in a variety of mixed random variables. The main results we have obtained: almost sure convergence of the sequence of NA random variables and the Chover's law of the iterated logarithm of random variables with an exponent in （0，2） and 2, the Marcinkiewicz-type and Jamison-type strong law of large numbers for pairwise NQD sequences, the strong consistency of M estimators in linear models for ND random errors and mixed under the conditions of weak moments, some equivalent conditions of almost sure convergence and Chover type law of the iterated logarithm of partial sums of mixing sequence, some strong limit theorems for weighted product sums of mixing sequences of random variables, some limit theorems for sums of matrix sequences, recurrent, ergodicity properties for an extended birth-death minimal -process, etc. Most of these results have reached the desired results of independent case. We have already published or have been recruited 7 papers in the SCI journal, and published 19 papers in the core journals.In addition, we also obtained the almost sure central limit theory for the partial sums and products of partial sums with stable distribution, submited 2 papers to SCI journals, are among reviewers.These research results has a certain theoretical and practical significance on the Markov process of development of the theory. .The project training 22 graduate students, of whom 12 have graduated, these students are involved in the research work of this project, preliminary research has an independent ability to get a lot of research papers have been published or hire 29.

马氏过程的极限理论有着重要的理论意义和很强的应用背景，是概率极限理论的热点研究内容之一，本项目主要研究了马氏过程中各种混合随机变量的极限理论，获得的主要结果有：NA随机变量序列的几乎处处收敛性和特征指数属于（0，2）和2的Chover型重对数率，两两NQD随机变量序列的Marcinkiewicz型和Jamison型强大数律，线性模型ND随机误差等的M估计在较弱矩条件下的强相合性，混合序列部分和的几乎处处收敛的一些等价条件和Chover型k重对数率，加权乘积和的强极限定理，阵列行和的若干极限定理，广义生-灭最小Q过程的常返、遍历性等等，以上这些成果大部分都达到了独立情形的理想结果，已在SCI期刊源发表或录用论文7篇，在核心刊物发表论文19篇；另外，还获得了平稳过程的部分和以及部分和的乘积的几乎处处中心极限定理，已向SCI期刊投稿2篇，正在审稿之中。这些研究成果对马氏过程理论的发展有着一定的理论和实际意义。本项目培养研究生22人，其中已毕业12人，这些研究生都参与了本项目的研究工作，初步具备了独立做研究的能力，取得了不少的研究成果，已发表或录用的论文29篇。