1.

The precise asymptotics of the complete convergence for moving average processes of m dependent B valued elements





Xi Li Tan and Xiao Yun Yang《数学学报(英文版)》,2009年第25卷第3期


Let {εt;t ∈ Z} be a sequence of mdependent Bvalued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.

2.

Changepoint Estimation of a Mean Shift in Movingaverage Processes Under Dependence Assumptions





Yunxia Li《应用数学学报(英文版)》,2006年第22卷第4期


In this paper we discuss the leastsquare estimator of the unknown change point in a mean shift for movingaverage processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρmixing, φmixing, αmixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜ 〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.

3.

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS





林正炎 李德柜《数学物理学报(B辑英文版)》,2008年第28卷第1期


Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξtk, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

4.

A general result on precise asymptotics for linear processes of positively associated sequences 被引次数：2





Xili Tan and Xiaoyun Yang《高校应用数学学报(英文版)》,2008年第23卷第2期


Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεtj,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.

5.

Precise asymptotics of complete moment convergence on moving average





Zheng Yan Lin Hui Zhou《数学学报(英文版)》,2012年第28卷第12期


Let {ξi,∞i∞} be a doubly infinite sequence of identically distributedmixing random variables with zero means and finite variances,{ai,∞i∞} be an absolutely summable sequence of real numbers and X k =∑i=∞+∞ aiξi+k be a moving average process.Under some proper moment conditions,the precise asymptotics are established for

6.

The Convergence of a Moving Average Process of AANA Random Variables





TAN Jiaxin HUANG Qian HU Qi YANG Wenzhi《数学季刊》,2017年第2期


Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1+Y )] < ∞. As an application, MarcinkiewiczZygmundtype strong law of large numbers for this moving average process is presented in this paper.

7.

A general law of precise asymptotics for products of sums under dependence





Yong Zhang Xiao Yun Yang Zhi Shan Dong《数学学报(英文版)》,2010年第26卷第1期


Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.

8.

Some Limit Results for Moving Sums of Stable Random Variables





陈平炎《东北数学》,2004年第1期


We discuss the integral test for a moving sum of an iid symmetric stable sequence with exponent α (0 < α < 2), and the Chovertype LIL is given as a corollary. We also obtain the law of a single logarithm for moving sums of a normal sequence.

9.

Precise Asymptotics in the Law of the Iterated Logarithm of MovingAverage Processes 被引次数：1





Yun Xia LI Li Xin ZHANG《数学学报(英文版)》,2006年第22卷第1期


In this paper, we discuss the movingaverage process Xk = ∑i=∞ ^∞ ai＋kεi, where {εi;∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψmixing or negatively associated random variables with mean zeros and finite variances, {ai;∞ 〈 i 〈 ∞） is an absolutely solutely summable sequence of real numbers.

10.

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVYTAILED STEPS AND ITS APPLICATION TO RISK THEORY





王定成 苏淳《数学物理学报(B辑英文版)》,2007年第27卷第1期


In this article, the dependent steps of a negative drift random walk are modelled as a twosided linear process Xn =μ ∞∑j=∞ψnjεj, where {ε, εn; ∞＜ n ＜ ∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;∞＜ i ＜∞} satisfy 0 ＜∞∑j=∞jψj ＜∞. Under the conditions that the distribution function of ε has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(nμ ∞∑j=∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.

11.

随机游动局部时的某些极限性质





闻继威 严云良《高校应用数学学报(英文版)》,2006年第21卷第1期


Let X,X1,X2,...be i.i.d.random variables with EX2 δ<∞(for some δ>0).Consider a onedimensional random walk S={Sn}n≥0,starting from S0=0.Let ξk]=x}.A strong approximation of ξ*(n) by the local time for Wiener process is presented and the limsuptype and liminftype laws of iterated logarithm of the maximum local time ξ*(n) are obtained.Furthermore,the precise asymptotics in the law of iterated logarithm of ξ*(n) is proved.

12.

Testing for changes in the mean or variance of long memory processes





Yun Xia Li Jian Jun Xu Li Xin Zhang《数学学报(英文版)》,2010年第26卷第12期


In this paper, we study the asymptotic CUSUM tests for detecting changes in the mean or variance of a movingaverage process with long memory. When there is no change over [O,T], the asymptotic distribution of the test statistic is derived, which allows us to find asymptotic critical values. When there is a change, the behavior of the test statistic is discussed. Conditions for the consistency of these tests are also discussed. Based on the asymptotic results, simulation studies of testing for changes in the mean show that the CUSUM test proposed performs well.

13.

Law of nonlinear flow in saturated clays and radial consolidation 被引次数：4





邓英尔 谢和平 黄润秋 刘慈群《应用数学和力学(英文版)》,2007年第28卷第11期


It was derived that microscale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media.There is good agreement between the derived results and test ones.Results of experiments show that flow in microscale pore of saturated clays follows law of nonlinear flow.Theoretical analyses demonstrate that an interaction of solidliquid interfaces varies inversely with permeability or porous radius.The interaction is an important reason why nonlinear flow in saturated clays occurs.An exact mathematical model was presented for nonlinear flow in microscaie pore of saturated clays.Dimension and physical meanings of parameters of it are definite.A new law of nonlinear flow in saturated clays was established.It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one.Darcy law is a special case of the new law.A math ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow.Equations of average mass conservation and moving boundary,and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer,a method of steady state in stead of transient state and a method of integral of an equation.Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained.Re suits show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay.The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases.Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

14.

Convergence rates for probabilities of moderate deviations for moving average processes





Ping Yan Chen Ding Cheng Wang《数学学报(英文版)》,2008年第24卷第4期


The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some wellknown results.

15.

Precise Asymptotics for Lévy Processes





Zhi Shui HU Chun SU《数学学报(英文版)》,2007年第23卷第7期


Let {X（t）, t ≥ 0} be a Lévy process with EX（1） = 0 and EX^2（1） 〈 ∞. In this paper, we shall give two precise asymptotic theorems for {X（t）, t 〉 0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d. random variables.

16.

RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVINGAVERAGE PROCESSES





Li Yunxia Zhang Lixin《高校应用数学学报(英文版)》,2005年第20卷第4期


In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the movingaverage processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of changepoints estimation is derived. The result is also true for pmixing, φmixing, amixing, associated and negatively associated sequences under suitable conditions.

17.

Almost sure central limit theorems for random functions





LU Chuanrong QIU Jin & XU Jianjun School of Mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China Department of Mathematics Zhejiang University Hangzhou 310028 China《中国科学A辑(英文版)》,2006年第49卷第12期


Let {Xn,∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn ERn <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/22γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the functiontyped almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for Ustatistics, VonMises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, productlimit estimators of a continuous distribution, productlimit estimators of a quantile function, etc.

18.

LIL behavior for Bvalued strong mixing random variables





FU KeAng & ZHANG LiXin School of Statistics Mathematics Zhejiang Gongshang University Hangzhou China《中国科学 数学(英文版)》,2011年第4期


Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.

19.

Spatial Density Distributions and Correlations in a QuasioneDimensional Polydisperse Granular Gas





CHEN ZhiYuan ZHANG DuanMing《理论物理通讯》,2009年第51卷第2期


By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi onedimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a powerlaw form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.

20.

Chaos game representation （CGR）walk model for DNA sequences 被引次数：1





高洁 徐振源《中国物理 B》,2009年第18卷第1期


Chaos game representation(CGR) is an iterative mapping technique that processes sequences of units,such as nucleotides in a DNA sequence or amino acids in a protein,in order to determine the coordinates of their positions in a continuous space.This distribution of positions has two features:one is unique,and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences.A CGRwalk model is proposed based on CGR coordinates for the DNA sequences.The CGR coordinates are converted into a time series,and a longmemory ARFIMA(p,d,q) model,where ARFIMA stands for autoregressive fractionally integrated moving average,is introduced into the DNA sequence analysis.This model is applied to simulating real CGRwalk sequence data of ten genomic sequences.Remarkably longrange correlations are uncovered in the data,and the results from these models are reasonably fitted with those from the ARFIMA(p,d,q) model.
