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On the stability of diffusion processes with state-dependent switching

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science china Mathematics 2006年第9期49卷 1258-1274页

作者： XI Fubao & ZHAO Liqin Department of Mathematics, beijing Institute of Technology, beijing 100081, china school of mathematical sciences, beijing normal university, beijing 100875, china Department of Mathematics Beijing Institute of Technology Beijing 100081 China school of mathematical sciences Beijing Normal University Beijing 100875 China

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.

关键词： Feller continuity, coupling, strong Feller continuity, exponential ergodicity,state-dependent switching.

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

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Acta Mathematica Scientia 2011年第4期31卷 1494-1502页

作者：马宇韬 school of mathematical sciences Beijing Normal University

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal... 详细信息

关键词： W 1 H inequality T p (C)-inequality weakly dependent sequences tensorization

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

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Acta Mathematica Scientia 2006年第2期26卷 229-245页

作者：唐仲伟 school of mathematical sciences beijing normal university Beijing 100875China

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3, x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2）〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically ***, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

关键词： Cylindrical symmetry asymptotic behavior ground state solution

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 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 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

Birth-death processes on trees

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science china Mathematics 2010年第11期53卷 2993-3004页

作者： MA YuTao school of mathematical sciences & Laboratory of Mathematics and Complex Systems, beijing normal university, beijing 100875, china 1. school of mathematical sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z+, we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue λ0. At last, some examples are investigated to justify our results.

关键词： birth-death process tree ergodicity Dirichlet eigenvalue

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

Representation type of 0-Hecke algebras

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science china Mathematics 2011年第3期54卷 411-420页

作者： DENG BangMing1 & YANG GuiYu2,1Department of Mathematics, beijing normal university, beijing 100875, china 2school of science, Shangdong university of Technology, Zibo 255049, china 1. Department of Mathematics Beijing Normal University Beijing 100875 China2. School of Science Shangdong University of Technology Zibo 255049 China

In the present paper we determine the representation type of the 0-Hecke algebra of a finite Coxeter group.

关键词： Coxeter group 0-Hecke algebra representation type

Functional central limit theorem for super α-stable processes

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science china Mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of Mathematics, beijing normal university, beijing 100875, china 1. Department of Mathematics Beijing Normal University 100875 Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α 2α (0 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d 2α, the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

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.