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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 m-dependent B-valued 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.  Change-point Estimation of a Mean Shift in Moving-average Processes Under Dependence Assumptions  
   Yun-xia Li《应用数学学报(英文版)》,2006年第22卷第4期
   In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average 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 ρ-mixing, φ-mixing, α-mixing 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 αkξt-k, 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
   Xi-li Tan and Xiao-yun 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^∞ ajεt-j,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 distributed-mixing 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 Jia-xin  HUANG Qian  HU Qi  YANG Wen-zhi《数学季刊》,2017年第2期
   Based on the asymptotically almost negatively associated(AANA) random vari-ables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1+Y )] < ∞. As an application, Marcinkiewicz-Zygmund-type 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 Chover-type 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 Moving-Average 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 moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing 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 HEAVY-TAILED 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 two-sided linear process Xn =-μ ∞∑j=-∞ψn-jεj, 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 one-dimensional 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 limsup-type and liminf-type 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 moving-average 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 micro-scale 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 micro-scale pore of saturated clays follows law of nonlinear flow.Theoretical analyses demonstrate that an interaction of solid-liquid 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 micro-scaie 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 well-known 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 MOVING-AVERAGE 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 moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, 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 E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed 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 U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.    

18.  LIL behavior for B-valued 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 Quasi-one-Dimensional Polydisperse Granular Gas  
   CHEN Zhi-Yuan ZHANG Duan-Ming《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 one-dimensional 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 power-law 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 CGR-walk model is proposed based on CGR coordinates for the DNA sequences.The CGR coordinates are converted into a time series,and a long-memory 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 CGR-walk sequence data of ten genomic sequences.Remarkably long-range correlations are uncovered in the data,and the results from these models are reasonably fitted with those from the ARFIMA(p,d,q) model.    

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