关于随机变量矩的两个不等式

推广了随机变量的Hder矩不等式和Minkowski矩不等式.即得到了下列两个新的不等式:广义Hder矩不等式和广义Minkowski矩不等式.在理论和应用上都具有一定的价值.

随机变量的矩在证明积分不等式中的应用

概率论不仅广泛运用于应用学科,而且在基础数学中也有着重要应用.基础数学中一些重要的定理、公式、不等式等都可以用概率论的方法得到证明.文〔1〕利用概率方法证明了一些代数不等式.本文主要利用概率中随机变量矩的一些重要不等式证明了一些重要的积分不等式,具有直观性、可行性和简便性.

关于非负随机变量的几个矩不等式

设X是非负随机变量且0<m≤X≤M,本文讨论两个Cauchy型矩不等式的反向,得到以下不等式:E(X2)-(E(X))2≤41(M-m)2,E(X2)-E(X)≤4((M M-+mm))2,E(X)-(E(X-1))-1≤(M-m)2,E(X)E(X-1)≤(M4+Mmm)2,并利用所得结果给出一些反向Cauchy-Schwarz不等式.

模糊随机桁架结构在模糊随机激励下的动力响应

研究了模糊随机参数桁架结构在模糊随机荷载激励下的复合模糊随机振动动力响应的问题。同时考虑结构的物理参数、几何尺寸和外载荷幅值的模糊随机性,从Duham e l积分式出发,利用振型迭加法求出了结构动力响应模糊随机变量的表达式;再由随机函数的矩法推导出结构模糊随机动力响应的模糊数字特征。最后,通过算例考察了结构参数和作用荷载的模糊随机性对结构动力响应的影响,并用M on te C arlo数值法对算例进行模拟,验证了文中模型和分析方法是可行有效的。

Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

特征函数与矩的存在性的关系

摘要:本文应用随机变量的特征函数讨论了随机变量的矩的存在性,阐述了它们之间的关系。

Reliability analysis of earth slopes using hybrid chaotic particle swarm optimization

A numerical procedure for reliability analysis of earth slope based on advanced first-order second-moment method is presented,while soil properties and pore water pressure may be considered as random variables.The factor of safety and performance function is formulated utilizing a new approach of the Morgenstern and Price method.To evaluate the minimum reliability index defined by Hasofer and Lind and corresponding critical probabilistic slip surface,a hybrid algorithm combining chaotic particle swarm optimization and harmony search algorithm called CPSOHS is presented.The comparison of the results of the presented method,standard particle swarm optimization,and selected other methods employed in previous studies demonstrates the superior successful functioning of the new method by evaluating lower values of reliability index and factor of safety.Moreover,the presented procedure is applied for sensitivity analysis and the obtained results show the influence of soil strength parameters and probability distribution types of random variables on the reliability index of slopes.

基于特征函数教学的一点思考

作为描述随机变量分布的重要工具,特征函数包含了分布函数所有矩的信息。基于概率论与数理统计教学,结合定义和两个重要性质,阐述了特征函数在重要分布可加性以及随机变量矩计算方面的应用。

A Probabilistic Interpretation to Umbral Calculus

A natural simple interpretation to the umbral calculus is given. As an application, a simple umbral proof of Abel identity is obtained.

Moment Bounds for Strong Mixing Sequences and Their Application

Some moment inequalities for the strong mixing random variable sequence are established, and applied to discuss the asymptotic normality of the general weight function estimate for the fixed design regression model.

The Law of the Iterated Logarithm for Independent Random Variables with Multidimensional Parameters and Its Application

For a set of i.i.d.r.v. indexed by positive integer d-dimensional lattice points, and for some general normalizing sequence, we determine necessary and sufficient conditions for the law of iterated logarithm. As its application, we give conditions for the existence of moments of the supremum of normed partial sums.

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved