Variance and exponential estimates via coupling

We give a proof of Devroye and exponential inequalities based on a coupling. We mostly deal with the case of continuous random variables with dynamical systems in mind (and their rather special mixing properties) although the approach is more general.     

马氏过程函数的强大数定律

本文主要研究了马氏过程函数以及马氏环境中马氏链函数的强大数定律．     

New large sets of t‐designs with prescribed groups of automorphisms

In this article, we investigate the existence of large sets of 3‐designs of prime sizes with prescribed groups of automorphisms PSL(2,q) and PGL(2,q) for q < 60. We also construct some new interesting large sets by the use of the computer program DISCRETA. The results obtained through these direct methods along with known recursive constructions are combined to prove more extensive theorems on the existence of large sets. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 210–220, 2007     

经验测度序列的大偏差原理

设{X_i,i∈N)是平稳N A随机变量序列且ψ_(1)＞0．记经验测度δ_n=1/n■,借助于弱收敛拓扑下的开集与β度量下的开球之间的关系,证明了{P{δ_n∈·},n→∞}在(M_1(R),■)上满足大偏差原理．     

Extra dimension searches at hadron colliders to next-to-leading order-QCD

The quantitative impact of NLO-QCD corrections for searches of large and warped extra dimensions at hadron colliders are investigated for the Drell-Yan process. The K-factor for various observables at hadron colliders are presented. Factorisation, renormalisation scale dependence and uncertainties due to various parton distribution functions are studied. Uncertainties arising from the error on experimental data are estimated using the MRST parton distribution functions.      

Deviations bounds and conditional principles for thin sets

The aim of this paper is to use non-asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to stochastic mechanics and calibration problems for diffusion processes are discussed.     

最佳投资策略下投资额函数的渐近性质

本文考虑一个经典风险模型,且允许保险公司投资股票市场,通过选择适当的投资策略使破产概率达到最小,并求出当分布函数F(x)是正则变化函数时,投资额函数A(x)的近似表达式.     

On the Distance Between Some πps Sampling Designs

Asymptotic distances between probability distributions appearing in πps sampling theory are studied. The distributions are Poisson, Conditional Poisson (CP), Sampford, Pareto, Adjusted CP and Adjusted Pareto sampling. We start with the Kullback-Leibler divergence and the Hellinger distance and derive a simpler distance measure using a Taylor expansion of order two. This measure is evaluated first theoretically and then numerically, using small populations. The numerical examples are also illustrated using a multidimensional scaling technique called principal coordinate analysis (PCO). It turns out that Adjusted CP, Sampford, and adjusted Pareto are quite close to each other. Pareto is a bit further away from these, then comes CP and finally Poisson which is rather far from all the others.      

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

M-negatively associated random variables,which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its par- ticular case,are introduced and studied.Large deviation principles and moderate devi- ation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.     

P. L. Chebyshev的概率新思想溯源

切贝舍夫是俄国十九世纪最伟大的数学家之一,他第一个主张概率论的极限定理应该严格的证明,并尽可能精确地确定偏离极限的估计量,这在方法论上引起了很大变化.其创立的切贝舍夫不等式和切贝舍夫大数定律是概率论极限理论的基础,从而使概率论成为严密数学分支.切贝舍夫的概率思想是在一定数学文化背景产生的,尤其是法国数学文化对其发展的形成有着深刻影响.