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Laws of the Iterated Logarithm for Locally Square Integrable Martingales

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Acta Mathematica Sinica,English Series 2009年第2期25卷 209-222页

作者： fu qing GAO School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

Three types of laws of the iterated logarithm （LIL） for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a numbe... 详细信息

关键词： locally square integrable martingales law of the iterated logarithm

Laws of the Iterated Logarithm for High-Dimensional Wiener Sausage

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1599-1610页

作者： Yan qing WANG fu qing GAO School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

Let {β（s）,s ≥ O} be the standard Brownian motion in R^d with d ≥ 4 and let ｜Wr（t）｜ be the volume of the Wiener sausage associated with {β（s）, s ≥ O} observed until time t. Prom the central limit theorem of Wiener sausage, we know that when d ≥ 4 the limit distribution is normal. In this paper, we study the laws of the iterated logarithm for ｜Wr（t）｜ - e｜Wr（t）｜ in this case.

关键词： Wiener sausage Kolmogorov's law of the iterated logarithm Chung's law of the iterated logarithm

Treatment of simulated wastewater containing Reactive Red 195 by zero-valent iron/activated carbon combined with microwave discharge electrodeless lamp/sodium hypochlorite

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Journal of Environmental Sciences 2010年第4期22卷 512-518页

作者： Jie fu Zhen Xu qing-Shan Li Song Chen Shu-qing An qing-fu Zeng Hai-Liang Zhu State Key Laboratory of Pharmaceutical Biotechnology School of Life Sciences Nanjing University Nanjing 210093 China. Engineering Research Center for Clean Production of Textile Dyeing and Printing of Ministry of Education Wuhan University of Scienee & Engineering Wuhan 430073 China Pharmacy Department Shanghai Hospital of Skin Diseases and Sexually Transmitted Diseases Shanghai 200443 China

A comparative study of treatment of simulated wastewater containing Reactive Red 195 using zero-valent iron/activated carbon （ZVI/AC）, microwave discharge electrodeless lamp/sodium hypochlorite （MDEL/NaCIO） and the combination of ZVI/AC- MDEL/NaCIO was conducted. The preliminary results showed the two steps method of ZVI/AC-MDEL/NaCIO had much higher degradation efficiency than both single steps. The final color removal percentage was nearly up to 100% and the chemical oxygen demand reduction percentage was up to approximately 82%. The effects of operational parameters, including initial pH value of simulated wastewater, ZVI/AC ratio and particle size of ZVI were also investigated. In addition, from the discussion of synergistic effect between ZVI/AC and MEDL/NaCIO, we found that in the ZVI/AC-MEDL/NaCIO process, ZVI/AC could break the azo bond firstly and then MEDLfNaCIO degraded the aromatic amine products effectively. Reversing the order would reduce the degradation efficiency.

关键词： activated carbon microwave discharge electrodeless lamp Reactive Red 195 sodium hypochlorite zero-valent iron.

Energetic Argument for Bimodal Black Hole Accretion discs

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Chinese Physics Letters 2002年第10期19卷 1562-1564页

作者： Lin Yi-qing, Lu Ju-fu Department of Physics Xiamen University Xiamen 361005

Based on simple energetic considerations, we show that two crucial ingredients of bimodal black hole accretion discs, namely the sonic point and the transition radius, can be determined from the disc constant paramete... 详细信息

关键词： Black holes Instability

Precise Deviations for Discrete Ensembles

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1580-1596页

作者： Wen Xuan CHEN fu qing GAO School of Mathematics and Statistics Wuhan UniversityWuhan 430072P.R.China

We consider precise deviations for discrete ***β=2 case,we first establish an asymptotic formula of the Christoffel–Darboux kernel of the discrete orthogonal polynomials on an infinite regular lattice with weight e^(−NV(x)).Then we use the asymptotic formula to get the precise deviations of the extreme value for corresponding ensemble.

关键词： Discrete ensemble precise deviation random growth model Riemann-Hilbert problem

The Support of the Solution for Stochastic Differential Equations Driven by G-Brownian Motion

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2417-2430页

作者： fu qing GAO Ming Zhou XU Department of Mathematics and Statistics Wuhan University

By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.

关键词： G-Brownian motion G-stochastic differential equation support theorem

Local functional Limit Theorems of Increments for Brownian Motion

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1074-1086页

作者： fu qing GAO Yong Hong LIU School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 541004 P. R. China

In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of contin... 详细信息

关键词： Keywords Brownian motion increment local functional limit rate of convergence large deviation small deviation

Large Deviations for Parameter Estimators of Some Time Inhomogeneous Diffusion Process

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2245-2258页

作者： Shou Jiang ZHAO fu qing GAO School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China School of Science China Three Gorges University Yichang 443002 P. R. China

The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by ... 详细信息

关键词： Parameter estimation large deviations time inhomogeneous diffusion process

Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data

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Acta Mathematica Sinica,English Series 2010年第5期26卷 937-950页

作者： fu qing GAO Li Na LI School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China Department of Mathematics Tongji University Shanghai 200092 P. R. China

Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for {sup x∈sd-1 ｜fn（x） - E（fn（x））｜, n ≥ 1} hold.

关键词： kernel density estimator directional data moderate deviations large deviations