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A fiducial argument for generalized p-value

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Science china mathematics 2007年第7期50卷 957-966页

作者： Xin-min LI~(1+) Xing-zhong XU~2 Guo-ying LI~3 1 institute of Applied mathematics,Shandong University of technology,Zibo 255049,china 2 department of mathematics,beijing institute of technology,beijing 100801,china 3 Academy of mathematics and Systems Science,Chinese Academy of Sciences,beijing 100800,china institute of Applied mathematics Shandong University of Technology Zibo 255049 China department of mathematics Beijing Institute of Technology Beijing 100801 China Academy of Mathemtics Systems Science Chinese Academy of Sciences Beijing 100800 China

This paper provides a general method for constructing generalized p-value via the fiducial ***,the power properties of the generalized test are *** illustrations, the two-parameter exponential distribution and unbalan... 详细信息

关键词： fiducial distribution generalized p-value frequency property two-parameter exponential distribution variance component 62F03 62E15

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 1. department of mathematics Beijing Institute of Technology Beijing 100081 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

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 1. department of mathematics Beijing Institute of Technology Beijing 100081 China 2. Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 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 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.

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 1. department of Applied mathematics Beijing Institute of Technology 100081 Beijing China

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

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

Dynamic information theory and information description of dynamic systems

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 607-627页

作者： XING XiuSan department of Physics, beijing institute of technology, beijing 100081, china 1. department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes, and that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production

关键词： dynamic information evolution equation informationization of dynamic equation information wave information flow and force information dissipation and production degradation and evolution

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

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Science china(Physics,Mechanics & Astronomy) 2010年第12期53卷 2194-2215页

作者： XING XiuSan department of Physics, beijing institute of technology, beijing 100081, china 1. department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or anothe

关键词： stochastic velocity type’s Langevin equation in 6N dimensional phase space drift-diffusion duality nonequilibrium entropy evolution equation entropy diffusion formula for entropy production rate entropy change from internal interaction a