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Precise Rates in the Law of the Logarithm for the Moment Convergence in Hilbert Spaces

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Acta Mathematica Sinica,English Series 2009年第2期25卷 191-208页

作者： ke ang fu Li Xin ZHang Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China School of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310035 P. R. China

Let （X, Xn; n ≥1） be a sequence of i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with covariance operator ∑. Set Sn = X1 ＋ X2 ＋ ... ＋ Xn, n≥ 1. We prove that, for b 〉 -1, lim ε→0 ε^2（b＋1） ∞ ∑n=1 （logn）^b/n^3/2 E{｜｜Sn｜｜-σε√nlogn}=σ^-2（b＋1）/（2b＋3）（b＋1） B｜｜Y｜^2b＋3holds if EX=0,and E｜｜X｜｜^2（log｜｜x｜｜）^3bv（b＋4）〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑.

关键词： the law of the logarithm moment convergence tail probability strong approximation

A Nonclassical LIL for Geometrically Weighted Series in Banach Space

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Acta Mathematica Sinica,English Series 2013年第7期29卷 1413-1420页

作者： ke ang fu Xiao Rong Yang Wei HUang School of Statistics and Mathematics Zhejiang Gongshang University Department of Mathematics Zhejiang University

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali （in IEEE Trans. Inform. Theory 55： 5302-5316, 2009）. We also give another sufficient condition on block RIP for such recovery method： 58 〈 0.307.

关键词： Banach space geometrically weighted series nonclassical law of the iterated logarithm

Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model

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Acta Mathematicae Applicatae Sinica 2021年第3期37卷 539-547页

作者： ke-ang fu Xin-mei SHEN Hui-jie LI Department of Statistics Zhejiang University City CollegeHangzhou 310015China School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Shunfeng Express Shanghai 200120China

Consider a two-dimensional renewal risk model,in which the claim sizes{Xk;k≥1}form a sequence of *** of a non-negative random vector whose two components are *** that the claim sizes and inter-arrival times form a sequence of *** pairs,with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being *** a precise large-deviation formula of the aggregate amount of claims is obtained.

关键词： consistent variation extended regular variation large deviations size-dependence two-dimensional risk model

Convergence Rates of Tail Probabilities for Sums under Dependence Assumptions

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1591-1600页

作者： Xiao Rong Yang Wei Dong LIU ke ang fu Lin Xin ZHang School of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 P. R. China Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China School of Statistics and Mathematics Zhejiang Gongshang University Han qzhou 310018 P. R. China

Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）dx 〈∞ to hold is established, by using coupled methods together withstrong approximation, which are different from the traditional symmetrization and Hoffman-JФrgensen inequality.

关键词： Complete convergence mixing sequences strong approximation

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第4期8卷 651-659页

作者： fu ke-ang ZHang Li-xin Department of Mathematics Zhejiang University Hangzhou 310027 China

Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.

关键词： The law of the logarithm Random field Hilbert space. Tail probabilitv. Truncation method

A weak invariance principle for self-normalized products of sums of mixing sequences

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Applied Mathematics(A Journal of Chinese Universities) 2008年第2期23卷 183-189页

作者： fu ke-ang HUang Wei Dept. of Math. Zhejiang Univ. Hangzhou 310027 China

Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of ... 详细信息

关键词： self-normalized product domain of attraction of the normal law φ-mixing Wiener process.

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

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Applied Mathematics(A Journal of Chinese Universities) 2015年第3期30卷 347-360页

作者： fu ke-ang QIU Yu-yang Wang An-ding School of Statistics and Mathematics Zhejiang Gongshang University

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

关键词： by-claim dominatedly varying tail extended upper negative dependence quasi-asymptotic independence ruin probability time-depende

Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

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Applied Mathematics(A Journal of Chinese Universities) 2018年第4期33卷 491-502页

作者： SHEN Xin-mei fu ke-ang ZHONG Xue-ting School of Mathematical Sciences Dalian University of Technology School of Statistics and Mathematics Zhejiang Gongshang University

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

关键词： Precise large deviation Size-dependent Consistent variation Multidimensional risk model Renewal counting process

Structure of High Temperature Phase α-Ba_3Y(BO_3)_3 Crystal

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Chinese Journal of Structural Chemistry 2003年第5期22卷 550-552页

作者： PANShang-ke WangGuo-fu StatekeyLaboratoryofStructuralChemistry FujianInstituteofResearchontheStructureofMatterTheChineseAcademyofSciencesFuzhouFujian350002China GraduateSchooloftheChineseAcademyofSciences Beijing100039China

The high temperature phase a-Ba3Y(BO3)3 was synthesized by Czochralski method, and its crystal structure has been determined by single-crystal X-ray diffraction. It crystallizes in the trigonal system, space group 3R with a = 13.028(2), c = 9.4992(2) ? V = 1396.1(5) ?, Ba3YB3O9, Mr = 677.36, Z = 6, Dc = 4.834 g/cm3, l(MoKa) = 0.71073 ? m = 18.721 mm-1, F(000) = 1764, the final R = 0.0718 and wR = 0.1640 for 1199 observed reflections with I > 2s(I). In this structure two alternate nonequivalent Y atoms form one-dimensional chains bridged by the Ba atoms with BO3 triangles which link Y(1) and Y(2), respectively. The Ba atom is surrounded by nine O atoms belonging to six BO3 triangles.

关键词： synthesis crystal structure double borate