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A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series

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Acta Mathematica Sinica,English Series 2016年第3期32卷 384-392页

作者： ke ang FU Wei HUang School of Statistics and Mathematics Zhejiang Gongshang University Department of Mathematics Zhejiang University

Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I（｜X｜ ≤ x） is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞（n=0）β~nXn（0 〈 β 〈 1） is obtained, under some minimal conditions.

关键词： Domain of attraction of the normal law geometrically weighted series law of the iteratedlogarithm self-normalization slowly varying

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.

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

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

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

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

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

Motion direction prediction through spike timing based on micro Capsnet networks

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Science China(Technological Sciences) 2022年第11期65卷 2763-2775页

作者： ZHang HuaLiang LIU Ji Wang BaoZeng DAI Jun LIAN JinLing ke ang ZHAO YuWei ZHOU Jin Wang ChangYong Bejing Institute of Basic Medical Sciences Bejing 100850China School of Artificial Intlligence and Automation Huazhong University of Science and TechnologyWuhan 430074China

Neural activity extraction and neural decoding from neural signals are an important part of critical components of brain-computer interface *** the development of brain-computer interface technology,the demand for precise external control and nervous activities in macaque monkey during unilateral hand grasp has increased the complexity of control and neural decoding,which puts forward higher requirements for the accuracy and stability of feature extraction and neural *** this study,a micro Capsnet network architecture that consists of a few network layers,a vector feature structure,and optimization network parameters,is proposed to decrease the computing time and complexity,decrease artificial debugging,and improve the decoding *** with KNN,SVM,XGBOOST,CNN,Simple RNN,and LSTM,the algorithm in this study improves the decoding accuracy by 98.03%,and achieves state-of-the-art accuracy and stronger ***,the proposed algorithm can further enhance the control accuracy in the brain-computer interface.

关键词： spike timing micro Capsnet network brain-computer interface motion direction prediction optimized network parameter