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L^2-Algebraic Decay Rate for Transient Birth-Death Processes

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Chinese Annals of mathematics,Series B 2012年第4期33卷 583-594页

作者： Lijuan CHENG1 Yingzhe WANG2 1laboratory of mathematics and complex systems, the ministry of education of china School of Mathe-matical Sciences, beijing Normal University, beijing 100875, china. 2laboratory of mathematics and complex systems, the ministry of education of china School of Mathematical Sciences, beijing Normal University, beijing 100875, china. laboratory of mathematics and complex systems the Ministry of Education of China School of Mathematical Sciences Beijing Normal University Beijing China

This paper is a continuation of the study of the algebraic speed for Markov processes. The authors concentrate on algebraic decay rate for the transient birth-death processes. According to the classification of the boundaries, a series of the sufficient conditions for algebraic decay is presented. To illustrate the power of the results, some examples are included.

关键词： Transient Birth-death processes Algebraic decay

DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH

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Journal of systems Science & complexity 2010年第2期23卷 362-371页

作者： Jiao JIN·Hengjian CUI School of Mathematical Sciences,Key laboratory of mathematics and complex systems,ministry of education, beijing Normal University,beijing 100875,china. School of Mathematical Sciences Key Laboratory of Mathematics and Complex Systems Ministry of Education

In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been *** this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is *** aclassification rule based on the depth function family is *** classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.

关键词： Depth discriminant analysis location parameter MVE scatter matrix.

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

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Science china mathematics 2008年第3期51卷 343-350页

作者： HONG WenMing School of Mathematical Sciences, laboratory of mathematics and complex systems, ministry of education,beijing Normal University, beijing 100875, china School of Mathematical Sciences Laboratory of Mathematics and Complex Systems Ministry of Education Beijing Normal University Beijing China

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

关键词： super-Brownian motion large deviation moderate deviation random immigration Primary 60J80 Secondary 60F05

Convergence rates for reversible Markov chains without the assumption of nonnegative definite matrices

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Science china mathematics 2010年第8期53卷 1979-1988页

作者： MAO Yong-Hua School of Mathematical Sciences,beijing Normal University,laboratory of mathematics and complex systems,ministry of education,beijing 100875,china School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing China

Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed *** way by Lyapunov's drift conditions is also used to derive these convergence *** a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.

关键词： Markov chain spectral theory convergence rate geometric ergodicity strong ergodicity Lyapunov’s condition

Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel

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Science china mathematics 2010年第1期53卷 165-172页

作者： YANG Wei & LIU YongPing School of Mathematical Sciences,beijing Normal University laboratory of mathematics and complex systems,ministry of education,beijing 100875,china School of Mathematical Sciences Beijing Normal University laboratory of mathematics and complex systems Ministry of Education Beijing China

In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q a... 详细信息

关键词： relative n-width periodic convolution class NCVD-kernel B-kernel

Tail estimates for one-dimensional non-nearest-neighbor random walk in random environment

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Science china mathematics 2010年第9期53卷 475-484页

作者： GAO ZhiQiang 1,2 1 School of Mathematical Sciences, beijing Normal University, laboratory of mathematics and complex systems, ministry of education, beijing 100875, china 2 Laboratoire de Mathatiques et Applications des Mathmatiques, Universit de Bretagne-Sud, BP 573, Vannes 56017, France School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing China Laboratoire de Mathéatiques et Applications des Mathématiques Université de Bretagne-Sud Vannes France

Suppose that the integers are assigned i.i.d. random variables {(β gx , . . . , β 1x , α x )} (each taking values in the unit interval and the sum of them being 1), which serve as an environment. This environment defines a random walk {X n } (called RWRE) which, when at x, moves one step of length 1 to the right with probability α x and one step of length k to the left with probability β kx for 1≤ k≤ g. For certain environment distributions, we determine the almost-sure asymptotic speed of the RWRE and show that the chance of the RWRE deviating below this speed has a polynomial rate of decay. This is the generalization of the results by Dembo, Peres and Zeitouni in 1996. In the proof we use a large deviation result for the product of random matrices and some tail estimates and moment estimates for the total population size in a multi-type branching process with random environment.

关键词： random walks in random environment large deviations

Asymptotic distributions in the projection pursuit based canonical correlation analysis

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Science china mathematics 2010年第2期53卷 485-498页

作者： JIN Jiao & CUI HengJian Department of Statistics and Financial mathematics, School of Mathematical Sciences, beijing Normal University, laboratory of mathematics and complex systems (beijing Normal University), ministry of education, beijing 100875, china Department of Statistics and Financial mathematics School of Mathematical Sciences Beijing Normal University Beijing China ministry of education Laboratory of Mathematics and Complex Systems (Beijing Normal University) Beijing China

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and we... 详细信息

关键词： asymptotic distribution canonical correlation analysis influence function robust statistics

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science china mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2 & CUI HengJian 1,2 1 School of Mathematical Sciences,beijing Normal University,laboratory of mathematics and complex systems,ministry of education,beijing 100875,china 2 School of Mathematical Sciences,Capital Normal University,beijing 100048,china School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing China School of Mathematical Sciences Capital Normal University Beijing China

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

Quenched moderate deviations principle for random walk in random environment

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Science china mathematics 2010年第8期53卷 1947-1956页

作者： HONG WenMing 1 & WANG HuaMing 1,2 1 Key laboratory of mathematics and complex systems of ministry of education & School of Mathematical Sciences,beijing Normal University,beijing 100875,china 2 Department of Basic Courses,Business College,beijing Union University,beijing 100025,china Key laboratory of mathematics and complex systems of ministry of education & School of Mathematical Sciences Beijing Normal University Beijing China Department of Basic Courses Business College Beijing Union University Beijing China

We derive a quenched moderate deviations principle for the one-dimensional nearest random walk in random environment,where the environment is assumed to be stationary and *** approach is based on hitting time decompos... 详细信息

关键词： random walk in random environment moderate deviations principle hitting time