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行为NA的随机变量阵列加权和的完全收敛性

武汉大学学报（理学版） 2004年第3期50卷 287-290页

作者：邱德华甘师信衡阳师范学院数学系湖南衡阳421008 武汉大学数学与统计学院湖北武汉430072

{Xni,1≤i≤n,n∈N}是行为NA的随机变量阵列,且一致有界于随机变量X,p>0,E｜X｜2p2ni=o(1∞,EXni=0(1≤i≤n,n∈N),{ani,1≤i≤n,n∈N}是实数阵列,max｜ani｜=O(1logn),n1/p),∑n1≤i≤ni=1C0,推广了Stout及Taylor等相应的结果.

关键词：行为NA的随机变量阵列完全收敛一致有界于随机变量

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统计不变测度及其维数性质

武汉大学学报（理学版） 2002年第5期48卷 544-548页

作者：杨元启胡迪鹤三峡大学理学院湖北宜昌443002 武汉大学数学与统计学院湖北武汉430072

研究了Graf定义的统计自相似集的结构 ,提出了统计不变测度的概念 ,并得到了统计不变测度的支撑 ,以及它的维数和维数分布 .

关键词：统计自相似集统计不变测度维数维数分布概率测度随机过程

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随机环境Q过程的存在性

武汉大学学报（理学版） 2002年第5期48卷 549-552页

作者：田俊忠胡迪鹤西北第二民族学院信息与计算科学系宁夏银川750021 武汉大学数学与统计学院湖北武汉430072

研究了连续时间的可数状态的随机准转概阵的a .s.样本连续性及可微性 ,进而研究了随机环境Q过程的存在性并构造出最小的随机环境Q过程。

关键词：随机准转概阵随机准转强阵随机环境Q过程 a.s.样本连续性 a.s.样本可微性马氏过程

Non-Homogeneous Riemann Boundary Value Problem with Radicals

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wuhan university Journal of Natural Sciences 2002年第4期7卷 379-382页

作者： Lu Jian-ke school of mathematics and statistics,wuhan university,wuhan 430072, hubei,china school of mathematics and statistics Wuhan University Wuhan Hubei China

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t... 详细信息

关键词： Riemann boundary value problem branch points of radicals index order at infinity sectionally holomorphic functions

The construction of Markov processes in random environments and the equivalence theorems

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Science china mathematics 2004年第4期47卷 481-496页

作者： HU Diheschool of mathematics and statistics, wuhan university, wuhan 430072, china school of mathematics and statistics Wuhan University Wuhan China

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec.2, we construct the Markov process in random enviromment and skew product Markov process by p - m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.

关键词： radom transition function, p -m process, Markov process in random environment, skew product Markov process, density function.

Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

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Science china mathematics 2010年第11期53卷 2949-2972页

作者： ZHANG XiCheng school of mathematics and statistics, wuhan university, wuhan 430072, china school of mathematics and statistics Wuhan University Wuhan China

In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

关键词： smooth solutions stochastic partial differential equations stochastic Navier-Stokes equations

Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science china mathematics 2010年第6期53卷 1421-1434页

作者： LIU Li school of mathematics and statistics,wuhan university,wuhan 430072,china school of mathematics and statistics Wuhan University Wuhan China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying *** moderate deviations of partial sums are first *** results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum

Some Index Classes of Singularity of Vector Fields on Manifolds with Boundary

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wuhan university Journal of Natural Sciences 2002年第4期7卷 388-390页

作者： Xu Xu, Liu Heng-xing school of mathematics and statistics, wuhan university, wuhan 430072, hubei, china school of mathematics and statistics Wuhan University Wuhan Hubei China

V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.

关键词： adapted fields singularity index

A General Solution for a Class of Non-Homogeneous Recurrence Relations with Two Indices

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wuhan university Journal of Natural Sciences 2010年第4期15卷 287-291页

作者： YU Chang’an school of mathematics and statistics, wuhan university, wuhan 430072, hubei, china school of mathematics and statistics Wuhan University Wuhan Hubei China

In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a con... 详细信息

关键词： two indices non-homogeneous recurrence relation formula of general solution