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Feller property and exponential ergodicity of diffusion processes with state-dependent switching

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Science china mathematics 2008年第3期51卷 329-342页

作者： XI FuBao department of mathematics, beijing institute of technology, beijing 100081, china department of mathematics Beijing Institute of Technology Beijing China

In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.

关键词： Feller continuity Radon-Nikodym derivative strong Feller continuity exponential ergodicity state-dependent switching 60J60 34D25

Fiducial intervals of restricted parameters and their applications

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Science china mathematics 2005年第11期48卷 1567-1583页

作者： LI Xinmin, LI Guoying & XU Xingzhong College of mathematics and Information Sciences, Shandong University of technology, Zibo 255049, china Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100800, china department of mathematics, beijing institute of technology, beijing 100801, china College of mathematics and Information Sciences Shandong University of Technology Zibo China Academy of mathematics and System Sciences Chinese Academy of Sciences Beijing China department of mathematics Beijing Institute of Technology Beijing China

In practice, the unknown parameters are often restricted. This paper provides a general method for constructing the fiducial intervals of the restricted parameters. Applying the general method, the fiducial intervals are constructed for the location (scale)parameters and the difference (ratio) of two locations (scales) in a location (scale) family of distributions. The frequency properties of these intervals are verified. For a variance components model, the fiducial intervals for the three parameters of common interest are obtained. Their frequency properties are investigated theoretically and computationally.

关键词： restricted parameter space,fiducial interval,frequency property,variance components

ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEIGAO(department of Applied mathematics, beijing institute of technology, beijing 100081, china.) LI CUIZHE(department of Applied mathematics, beijing institute of technology, beijing 100081, china.) YU YUANHONG(Inditute of Applied mathematics, Acad department of Applied mathematics Beijing Institute of Technology Beijing 100081 China institute of Applied mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point

Fiducial inference in the pivotal family of distributions

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Science china mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying department of mathematics, beijing institute of technology, beijing 100081, china Academy of mathematics and Systems Science, Chinese Academy of Sciences, beijing 100080, china department of mathematics Beijing Institute of Technology Beijing China Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

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 China School of Mathematical Sciences Beijing Normal University Beijing 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.

The relative generalized Hamming weight and the semilinear equivalence of codes

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Science china(Information Sciences) 2011年第4期54卷 787-794页

作者： LIU ZiHui 1 & WANG Jie 2 1 department of mathematics,beijing institute of technology,beijing 100081,china 2 School of Mathematical Sciences,beijing University,beijing 100871,china department of mathematics Beijing Institute of Technology School of Mathematical Sciences Beijing University

Certain equivalent conditions are given for the semilinear equivalence of linear codes by using the relative generalized Hamming weight and the value function.

关键词： value function semilinear equivalence support weight relative generalized Hamming weight

Invariant Measures for a Random Evolution Equation with Small Perturbations

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Acta Mathematica Sinica,English Series 2001年第4期17卷 631-642页

作者： Fu Bao XI department of Applied mathematics, beijing institute of technology, beijing 100081, P. R. china department of Applied mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

关键词： Invariant measures Large deviations Coupling Random evolution equation

Dimension reduction based on weighted variance estimate

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Science china mathematics 2009年第3期52卷 539-560页

作者： ZHAO JunLong1 & XU XingZhong2 1 department of mathematics, Beihang University Laboratory of mathematics, Information and Behavior of the Ministry of Education, beijing 100083, china 2 department of mathematics, beijing institute of technology, beijing 100081, china department of mathematics Beihang University Laboratory of mathematics Information and Behavior of the Ministry of Education Beijing China department of mathematics Beijing Institute of Technology Beijing China

In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.

关键词： central subspace contour regression sliced average variance estimate sliced inverse regression sufficient dimension reduction weight function 62G08 62H05

A Fundamental Inequality for Meromorphic Functions in an Angular Domain and Its Application

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Acta Mathematica Sinica,English Series 1994年第3期10卷 308-314页

作者： Zhang Xuelian department of Applied mathematics beijing institute of technology beijing,100081 china beijing institute of technology

This paper is to study the characteristic functions of meromorphic functions for an angular *** show an inequality which is similar to the inequality in the second fundamental theorem of Nevranlinna,and estimate its *... 详细信息

关键词： inequality Borel Domain angular directions false suppose establishing latter enough