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On the law of the iterated logarithm for Brownian motion on compact manifolds

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Science China Mathematics 2019年第8期62卷 1511-1518页

作者： Cheng Ouyang Jennifer Pajda-De La O Department of Mathematics Statistics and Computer ScienceUniversity of Illinois at Chicago

By taking a functional analytic point of view,we consider a family of distributions(continuous linear functionals on smooth functions),denoted by{μt,t>0},associated to the law of the iterated logarithm for Brownian motion on a compact manifold.We give a complete characterization of the collection of limiting distributions of{μt,t>0}.

关键词： law of iterated logarithm compact manifold Brownian motion

A LAW OF THE ITERATED logarithm FOR NEIGHBOR-TYPE REGRESSION FUNCTION ESTIMATOR

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Chinese Annals of Mathematics,Series B 1992年第2期13卷 180-195页

作者：洪圣岩 Department of Mathematics Anhui University Hefei Anhui 230039 China

Let (X, Y) be a two-dimensional random variable. A law of the iterated logarithm is established for a smoothed neighbor-typo estimator of the regression function m(x)=E(Y|X=x) under conditions much weaker than needed for the Nadaraya-Watson estimator. Also the sharp pointwise rates of strong consistency of this estimator is discussed in detail.

关键词： estimator neighbor smoothed consistency kernel sharp logarithm iterated Watson bandwidth

Liminf law of the iterated logarithm for the smooth empirical distribution function

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Chinese Science Bulletin 1996年第3期41卷 185-189页

作者：周勇 Probability Laboratory Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).

关键词： liminf law of iterated logarithm smooth empirical distribution function.

Convergence in the law of logarithm for NA sequences

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Chinese Science Bulletin 1999年第15期44卷 1356-1360页

作者： Hanying Liang Chun Su Univ Sci & Technol China Dept Stat & Finance Hefei 230026 Peoples R China

Some results in the law of logarithm for NA sequences are obtained, which are similar to the result of id random variables; as a corollary, a sufficient result for the bounbed law of logarithm for NA arrays is given. Meanwhile, A conjecture for id random variables of Gut is answered in NA setting. Under weaker moment conditions than Su and Qin’s, a stronger convergence resuit than their Theorem 1 is obtained.

关键词： NA sequence law of logarithm convergence.

CONVERGENCE RATES OF LAW OF ITERATED logarithm FOR B-VALUED RANDOM VARIABLES

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Science China Mathematics 1991年第4期34卷 395-404页

作者：李德立 Department of Mathematics Jilin University Changchun 130023 PRC

Let {X, Xn; n≥1} be i.i.d.r.v.’s taking values in a separable Banach space （B,||·||）such that EX=0 and Ef2（X）*, and Sn=X1+…+Xn for n≥1. The purposeof this paper is to study the rates of convergence to zero of P(inf||Sn/（2nloglogn）1/2-x||≥ε) and P(sup inf||Sk/（2kloglogk）1/2-x||≥ε) （?ε>0） under precisely necessary and sufficientconditions. We also give new necessary and sufficient conditions for X to satisfy the boundand compact law of the iterated logarithm, respectively. Our results improve some resultsof Darling and Robbins （1967） as well as Davis （1968） even in the case B=R.

关键词： law of the iterated logarithm rate of convergence bounded in probability.

A LAW OF THE ITERATED logarithm FOR RANDOM WINDOW-WIDTH KERNEL ESTIMATOR OF A NONPARAMETRIC REGRESSION FUNCTION

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Systems Science and Mathematical Sciences 1990年第4期3卷 356-363页

作者：洪圣岩 Anhui University HefeiChina

In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These res... 详细信息

关键词： Regression function random window-width kernel estimator nearest neighbor estimator law of the iterated logarithm

LAWS OF THE ITERAFED logarithm FOR TRIMMED SUM

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Systems Science and Mathematical Sciences 1998年第1期11卷 39-46页

作者： PENG Liang(Deperttnent of Probebility and Statistics, Pebng University, Beijing 10087l, China)

In this paPer we shall give a theorem to explain the conjecture of P. S. G.iffin[1].

关键词： Law of the iterated logarithm trixnmed sum.

logarithm of a Function, a Well-Posed Inverse Problem

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American Journal of Computational Mathematics 2014年第1期4卷 1-5页

作者： Silvia Reyes Mora Víctor A. Cruz Barriguete Denisse Guzmán Aguilar Instituto de Física y Matemáticas Universidad Tecnológica de la Mixteca Huajuapan de León Oax México

It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is continuous in a domain , where is Hausdorff space and connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is fixed and is stable;for what in this case, the inverse problem turns out to be well-posed.

关键词： logarithm Function Inverse Problem Stability

Normal Contact Model for Elastic and Plastic Mechanics of Rough Surfaces

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Acta Mechanica Solida Sinica 2019年第2期32卷 148-159页

作者： Dong Wang Zhousuo Zhang Fan Jin Xuanhua Fan State Key Laboratory for Manufacturing and Systems Engineering School of Mechanical Engineering XVan Jiaotong University Xi'an 710049 China Institute of Systems Engineering China Academy of Engineering Physics Mianyang 621999 China

An elastic and plastic mechanical model is proposed to characterize the normal contact of rough surfaces. The contact process is considered as three separated contact regimes, i.e., the fully elastic, mixed elastic一plastic and fully plastic ones. The Hertzian elastic contact solutions and the classical fully plastic contact model of Abbott and Fires tone are used to model the contact behaviors of fully elastically deformed asperities and fully plastically deformed ones, respectively. For the mixed elastic-plastic regime, an improved Hermit interpolation method is applied to enforce the continuity and smoothness at the critical contact interference, and to decrease the interpolation waving effect by transforming the physical quantities of contact load into logarithmic coordinates. The contac t model of rough surfaces is formula ted by using the Greenwood and Williamson^ statistics analysis. Comparisons with the CEB, ZMC and KE models are then performed to examine the effects of plasticity index and mean separation. Agreeing well with the ZMC model, our results show that the total contact load of rough surfaces decreases with the increase in mean separation, and the difference between the prediction results of elastic models and the plastic ones also decreases, indicating that the contact behaviors mainly dominated by plastically deformed asperities have been changed to be controlled by elastically deformed ones. Larger plasticity index represents more plastically deformed asperities, inducing normal contact behaviors mainly dominated by plastic solutions.

关键词： Rough surfaces Elastic plastic Asperity contact logarithm transformation Statistics analysis