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Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

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Science China Mathematics 2008年第2期51卷 195-202页

作者： HUANG HuiLin~1 YANG WeiGuo~(2+) 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China 2 faculty of Science,Jiangsu University,Zhenjiang 212013,China 1. Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China 2. faculty of Science Jiangsu University Zhenjiang 212013 China

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded *** results generalize the analogous results on a homogene... 详细信息

关键词： Markov chains Shannon-McMillan theorem strong law of large numbers uniformly bounded tree 60f15 60J10

The Gaussian approximation for multi-color generalized friedman’s urn model

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Science China Mathematics 2009年第6期52卷 1305-1326页

作者： ZHANG LiXin HU feifang Department of Mathematics Zhejiang UniversityHangzhou 310027China Department of Statistics University of VirginiaHalsey HallCharlottesvilleVirginia 22904-4135USA

The generalized friedman’s urn model is a popular urn model which is widely used in many *** particular,it is extensively used in treatment allocation schemes in clinical *** this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized friedman’s urn model with both homogeneous and non-homogeneous generating *** Gaussian process is a solution of a stochastic differential *** Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical *** an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized friedman's urn model as well as the randomized-play-the-winner rule as a special case.

关键词： strong invariance Gaussian approximation the law of iterated logarithm asymptotic normality urn model randomized play-the-winner rule 60f15 62E20 62L05 60f05 62f12

Exponential inequalities for associated random variables and strong laws of large numbers

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Science China Mathematics 2007年第5期50卷 705-714页

作者： Shan-chao YANG & Min CHEN Deptartment of Mathematics, Guangxi Normal University, Guilin 541004, China Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China Deptartment of Mathematics Guangxi Normal University Guilin 541004 China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. for the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.

关键词： associated random variable exponential inequality strong law of large numbers rate of convergence 60E15 60f15

The application of spectral distribution of product of two random matrices in the factor analysis

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Science China Mathematics 2007年第9期50卷 1303-1315页

作者： Bai-suo JIN Bai-qi MIAO Wu-yi YE Zhen-xiang WU Department of Statistics and finance University of Science and Technology of ChinaHefei 230026China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080China

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of *** if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.

关键词： limiting spectral distribution product of random matrices large dimensional random matrices factor number time series 60f15 62H99

Maximal inequalities for demimartingales and their applications

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Science China Mathematics 2009年第10期52卷 2207-2217页

作者： WANG XueJun HU ShuHe School of Mathematical Science Anhui UniversityHefei 230039China

In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides. The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob’s type maximal inequality for demimartingales, strong laws of large numbers and growth rate for demimartingales and associated random variables. At last, we give an equivalent condition of uniform integrability for demisubmartingales.

关键词： maximal inequality demimartingales associated random variables growth rate 60E15 60f15

The exact Hausdorff measures for the graph and image of a multidimensional iterated Brownian motion

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Science China Mathematics 2007年第1期50卷 35-46页

作者： Rong-mao ZHANG Zheng-yan LIN Department of Mathematics Zhejiang UniversityHangzhou 310027China

Let {W (t), t ∈ R}, {B(t), t ∈ R +} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (X 1(t),…, X d (t)) and X 1(t),…, X d (t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q ? (0, ∞), the exact Hausdorff measures of the image X(Q) = {X(t): t ∈ Q} and the graph GrX(Q) = {(t, X(t)): t ∈ Q} are established.

关键词： graph Hausdorff measure image iterated Brownian motion sojourn time 60f15 60G15 60G17

Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications

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Science China Mathematics 2009年第9期52卷 1887-1904页

作者： YUAN DeMei AN Jun School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China

In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 f convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.

关键词： Rosenthal type inequality asymptotically almost negative association residual Cesàro α-integrability strong residual Cesàro α-integrability L p-convergence complete convergence Marcinkiewicz-Zygmund strong law 60f05 60f15

STRONG LAWS fOR α-MIXING SEQUENCE PROCESSES INDEXED BY SETS

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Applied Mathematics(A Journal of Chinese Universities) 1995年第1期10卷 45-48页

作者： XU BING Department of Mathematics Ningbo Normal College Ningbo

Let J = {1, 2,... }d and let {X j,j ∈J} be an a-mixing sequence which isnot necessarily stationary and let S(nA) be the sum of all Xj for which j/n ∈A. It isproved in this paper that S(·) satisfies the strong law o... 详细信息

关键词： 1991 MR Subject Classification 60f15