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partial sum of Dedekind sums

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Progress in Natural Science:Materials International 2000年第7期 73-79页

作者：张文鹏易媛 China The Research Center for Basic Science Xi’an 710049 Xi’an Jiaotong University

Using the mean square value formula of Dirichlet L-functions with the weight, the distribution property of the partial sum of Dedekind sums is studied. An interesting asymptotic formula is obtained.

关键词： Dedekind sums partial sum mean value distribution.

Moment inequalities for the partial sums of random variables

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Science China Mathematics 2001年第1期44卷 1-6页

作者：杨善朝 1. Department of Mathematics and Computer Science Guangxi Normal University 541004 Guilin China

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequali... 详细信息

关键词： partial sum M-Z-B type inequality Rosenthal type inequality

Joint Limit Distributions of Exceedances Point Processes and partial sums of Gaussian Vector Sequence

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1647-1662页

作者： Zuo Xiang PENG Jin Jun TONG Zhi Chao WENG School of Mathematics and Statistics Southwest University Department of Actuarial Science Faculty of Business and EconomicsUniversity of LausanneUNIL-Dorigny 1015 LausanneSwitzerland

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

关键词： Multivariate Gaussian sequence exceedances point process partial sum order statistic joint limit distribution

A Strong Approximation Theorem for Quasi-associated Sequences

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1269-1276页

作者： Wen Sheng WANG Department of Statistics East China Normal University Shanghai 200062 P. R. China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 P. R. China

By combining the Csorgo-Révész quantile transform methods and the Skorohod-Strassen martingale embedding theorem, we prove a strong approximation theorem for quasi-associated random variables with mean zero and finite （2 ＋ δ）th moment under polynomial decay rate. As a consequence, the decay rate for a strong approximation theorem of associated sequences of Yu （1996） is weakened.

关键词： Quasi-association partial sum Strong approximation Quantile transform

CONVERGENCE RATES IN THE LAW OF LOGARITHM OF RANDOM ELEMENTS

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Acta Mathematicae Applicatae Sinica 2001年第1期17卷 98-106页

作者：梁汉营苏淳王岳宝 Department of Applied Mathematics Tongji University Shanghai China University of Science and Technology of China Hefei China Department of Mathematics Suzhou University Suzhou China

We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space, and find the necessary and sufficient conditions on the convergence rates. The results of [1-3] for sums of i.i.d. real valued r.v.,s are extended; Yang's[4] result is generalized and the necessity part of Yang's result is also discussed; a conjecture for the i.i.d. real-valued r.v.s. of [5] is answered in Banach space.

关键词： Convergence rate logarithm law B-valued random element partial sum

A NOTE OF CONVERGENCE RATES FOR sumS OF ρ-MIXING SEQUENCES

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Acta Mathematicae Applicatae Sinica 1999年第2期15卷 172-177页

作者：梁汉营杨长森 Department of Mathematics Henan Normal University Xinxiang China Department of Statistics and Finance University of Science and Technology of China Hefei China

Let {Xn,n 1) be a sequence of mixing random variables, S(n)S, >0, d=1 *** note investigates that where is an arbitrary but fixed positive number. As application we give some results on the convergence rates for rand... 详细信息

关键词： mixing sequence partial sum convergence rate

POSITIVITY AND BOUNDEDNESS OF TRIGONOMETRIC sumS

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Analysis in Theory and Applications 2007年第4期23卷 380-388页

作者： Gavin Brown University of Sydney Australia

We give a systematic account of results which assure positivity and boundedness of partial sums of cosine or sine series. New proofs of recent results are sketched.

关键词： partial sum cosine series sine series orthogonal polynomials

ALMOST　EVERYWHERE　CONVERGENCE　AND　APPROXIMATION　OF　SPHERICAL　HARMONIC　EXPANSIONS

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Acta Mathematica Scientia 1995年第S1期15卷 109-122页

作者：李落清杨汝月 Department of Mathematics Hubei university Wuhan 430062 China Department of Mathematics Ningxia university Yinchuan 750021 China

This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of tho... 详细信息

关键词： Spherical harmonic series partial sum Convergence Approximation

On the Gibbs Phenomenon of Fourier Series of a Classical Function

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Journal of Mathematical Research and Exposition 2008年第2期28卷 347-352页

作者： XIANG Xue Yan HE Qian Department of Mathematics and Physics Lishui University Zhejiang 323000 China Department of Mathematics Zhejiang Normal University Zhejiang 321004 China

In this paper,we point out that the Fourier series of a classical function∑^∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of ***,we estimate the upper bound of its partial sum and get：sup n≥1｜｜∑^n ... 详细信息

关键词： Fourier series partial sum upper bound.