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Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science china mathematics 2010年第6期53卷 1421-1434页

作者： LIU Li school of mathematics and statistics,wuhan university,wuhan 4.0072,china 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying *** moderate deviations of partial sums are first *** results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum

The construction of Markov processes in random environments and the equivalence theorems

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Science china mathematics 2004年第4期47卷 481-496页

作者： HU Diheschool of mathematics and statistics, wuhan university, wuhan 4.0072, china 1. school of mathematics and statistics Wuhan University 430072 Wuhan China

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec.2, we construct the Markov process in random enviromment and skew product Markov process by p - m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.

关键词： radom transition function, p -m process, Markov process in random environment, skew product Markov process, density function.

Non-Homogeneous Riemann Boundary Value Problem with Radicals

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wuhan university Journal of Natural Sciences 2002年第4期7卷 379-382页

作者： Lu Jian-ke school of mathematics and statistics,wuhan university,wuhan 4.0072, Hubei,china wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t... 详细信息

关键词： Riemann boundary value problem branch points of radicals index order at infinity sectionally holomorphic functions

ON HASEMAN BOUNDARY VALUE PROBLEM FOR A CLASS OF META-ANALYTIC FUNCTIONS

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Acta Mathematica Scientia 2011年第1期31卷 39-48页

作者：汪玉峰杜金元 school of mathematics and statistics Wuhan University

In this article, Haseman boundary value problem for a class of meta-analytic functions is studied. The expression of solution and the condition of solvability for Haseman boundary value problem are obtained by changing the problem discussed into the equivalent Haseman boundary value problem of bi-analytic function. And the expression of solution and the condition of solvability depend on the canonical matrix.

关键词： Meta-analytic function bi-analytic function Haseman boundary value prob- lem canonical matrix

Weak martingale Hardy spaces and weak atomic decompositions

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Science china mathematics 2006年第7期49卷 912-921页

作者： HOU Youliang & REN Yanbo school of mathematics and statistics, wuhan university, wuhan 4.0072, china Department of mathematics & Physics, Henan university of Science and Technology, Luoyang 471003, china 1. school of mathematics and statistics Wuhan University Wuhan 430072 China 2. Department of mathematics & Physics Henan University of Science and Technology Luoyang 471003 China

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.

关键词： martingale, weak Hardy space, weak atom, atomic decomposition.

Adaptive quasi-likelihood estimate in generalized linear models

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Science china mathematics 2005年第6期48卷 829-846页

作者： CHEN Xia & CHEN Xiru school of mathematics and statistics, wuhan university, wuhan 4.0072, china Graduate school, Chinese Academy of Science, Beijing 100049, china 1. school of mathematics and statistics Wuhan University 430072 Wuhan China 2. Graduate school Chinese Academy of Science 100049 Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

Pinning control of general complex dynamical networks with optimization

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Science china(Information Sciences) 2010年第4期53卷 813-822页

作者： ZHAO JunChan, LU JunAn* & WU XiaoQun school of mathematics and statistics, wuhan university, wuhan 4.0072, china 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

This paper addresses optimal pinning control of general complex dynamical networks. A pinning scheme with linear feedback is proposed to globally exponentially stabilize a network onto a homogeneous state. In particular, we answer an important and fundamental question about pinning control: how to select an optimal combination between the number of pinned nodes and the feedback control gain? Three illustrative examples are provided to show the effectiveness of the proposed technique.

关键词： complex dynamical networks optimization pinning control linear feedback

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

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Science china mathematics 2004年第6期47卷 882-893页

作者： YUE Li & CHEN Xiru school of mathematics and statistics, wuhan university, wuhan 4.0072, china Graduate school, Chinese Academy of Sciences, Beijing 100039, china 1. school of mathematics and statistics Wuhan University 430072 Wuhan China 2. Graduate school Chinese Academy of Sciences 100039 Beijing China

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

关键词： quasi-likelihood function generalized linear models strong consistency

Dimensions of modified Besicovitch-Eggleston sets

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Science china mathematics 2006年第2期49卷 245-254页

作者： XIE Yuqiong & WEN Zhixiong Department of mathematics, wuhan university of Technology, wuhan 430070, china school of mathematics and statistics, wuhan university, wuhan 4.0072, china Department of mathematics Wuhan University of Technology Wuhan 430070 China school of mathematics statistics Wuhan University Wuhan 430072 China

We consider the variants of Besicovitch-Eggleston sets in symbolic spaces, and determine their fractal dimensions.

关键词： Besicovitch-Eggleston set fractal dimension symbolic space multifractal.