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Laws of iterated logarithm for transient random walks in random environments

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Frontiers of Mathematics in China 2015年第4期10卷 857-874页

作者： fuqing gao School of Mathematics and Statistics Wuhan University Wuhan 430072 China

We consider laws of iterated random walks in random environments. logarithm for one-dimensional transient A quenched law of iterated logarithm is presented for transient random walks in general ergodic random environm... 详细信息

关键词： Laws of iterated logarithm random walk random environment

Moderate deviations for estimators under exponentially stochastic differentiability conditions

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Frontiers of Mathematics in China 2018年第1期13卷 25-40页

作者： fuqing gao Qiaojing LIU School of Mathematics and Statistics Wuhan University Wuhan 430072 China

We introduce two exponentially stochastic differentiability conditions to study moderate deviations for M-estimators. Under a generalized exponentially stochastic differentiability condition, a moderate deviation principle is established. Some sufficient conditions of the exponentially stochastic differentiability and examples are also given.

关键词： M-estimator exponentially stochastic differentiability moderatedeviations

Deviation inequalities for quadratic Wiener functionals and moderate deviations for parameter estimators

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Science China Mathematics 2017年第7期60卷 1181-1196页

作者： gao fuqing JIANG Hui School of Mathematics and Statistics Wuhan University Wuhan 430072 China Hubei Key Laboratory of Computational Science Wuhan University Wuhan 430072 China Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation ***,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt *** applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.

关键词： quadratic Winer functional Laplace integral moderate deviations parameter estimator

Moderate deviations and hypothesis testing for signal detection problem

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Science China Mathematics 2012年第11期55卷 2273-2284页

作者： gao fuqing ZHAO ShouJiang School of Mathematics and Statistics Wuhan UniversityWuhan 430072China School of Science China Three Gorges UniversityYichang 443002China

Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-ατ（T）, where α〉 0, τ（T） = o（T） and τ（T）→∞ as the observation time T goes to infinity.

关键词： large deviations moderate deviations signal detection hypothesis testing

Weak entropy inequalities and entropic convergence

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Science China Mathematics 2008年第10期51卷 1798-1806页

作者： gao fuqing LI LiNa School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship t... 详细信息

关键词： entropic convergence particle system weak entropy inequality 60J25 37A35 82C22

Moderate deviations and central limittheorem for small perturbationWishart processes

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Frontiers of Mathematics in China 2014年第1期9卷 1-15页

作者： Lei CHEN fuqing gao Shaochen WANG School of Mathematics and Statistics Wulhan University Wuhan 430072 China

Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient： dXt^ε = √εXt^εtdBt＇＋ dBt＇√εXt^ε ＋ ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B＇ denotes the transpose of the matrix B. In this paper, we prove that { （Xt^ε-Xt^0）/√εh^2（ε）,ε 〉 0} satisfies a large deviation principle, and （Xt^ε - Xt^0）/√ε converges to a Gaussian process, where h（ε） → ＋∞ and √ε h（ε） →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method.

关键词： Large deviation moderate deviation central limit theorem Wishart vprocess eigenvalue

Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices.

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Science China Mathematics 2015年第9期58卷 1959-1980页

作者： CHEN Lei gao fuqing WANG ShaoChen School of Mathematics and Statistics Wuhan University School of Mathematics and Statistics Jiangsu Normal University

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.

关键词： random matrices eigenvalues Berry-Esseen bounds Cramér type large deviations

Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

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Wuhan University Journal of Natural Sciences 2008年第2期13卷 129-132页

作者： JIANG Hui gao fuqing School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be c... 详细信息

关键词： large deviations moderate deviations chi-square test

Deviation Inequality for the Number of k-Cycles in a Random Graph

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Wuhan University Journal of Natural Sciences 2009年第1期14卷 11-13页

作者： WANG Yanqing gao fuqing School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

We study the number of k-cycles in a random graph G（n, p）. We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By construct- ing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper.

关键词： random graph deviation inequality k-cycles