行—列可变换随机变量组列的极限定理

利用逆鞅、截尾等方法，我们得出行－列可变换随机变量组列的大数定律，作为推论，我们得到具有有限均值的行－列可变换无限组列满足强大数定律的充要条件是该组列的对角线元素不相关。再充分利用对称性及可变换性，我们得到对称可变换随机变量和的极限定理，并由此导出对称行－列可变换随机变量组列的完全收敛定理。     

具有不同分布NA随机变量列的强大数律及应用

给出了具有不同分布的NA随机变量列满足的若干强大数律;作为应用,不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形,而且关于NA随机变量的一些已有结果可以作为推论得出.     

Fourier变换在连续随机变量之和分布中的应用

本文给出了Fourier变换在求解相互独立的连续随机变量之和分布中的应用，证明了正态随机变量的可加性，方法简便、快速.这些充分显示了此工具的实用性.     

用积分变换法求连续型随机变量函数的密度函数

设X是一个连续型随机变量,其密度函数为px(x),g(x)是一个连续函数,给出了用积分变换求随机变量X的函数9(X)的密度函数的一个方法.该方法比传统的方法更简单.     

任意随机变量序列泛函及其随机变换的一类极限定理

采用鞅方法研究对任意随机变量序列普遍成立的强极限定理.并作为推论得到了m阶马氏过程,鞅序列,鞅差序列,独立随机变量序列的一类强极限定理.并把赌博系统的随机变换概念推广到任意随机变量序列的情况,得到任意随机变量序列随机选择与公平比的若干极限定理.     

随机变量的一种顺序及其应用

本文对分布于有限区间上的随机变量给出了一种顺序，并给出了其在实际中的一种应用．     

NA随机变量序列加权和的Chover型重对数律

利用NA随机变量的指数不等式,对于具有重尾分布的同分布的NA随机变量序列,得到了用积分检验来刻划其加权部分和的极限定理,作为推论还得到了Chover型重对数律.把这些结果应用到经典的可和方式,获得了相应的结果.这些结果推广了已知的一些结论.     

随机变量序更加权和的强收敛性

本文讨论一般随机变量序列加权和强收敛性，并为推论，得到一类鞅差序列加权和昨若干经典的独立随机变量序是的强大数定律，已有的若干结论是本文结果的特例。     

渐近正态随机变量函数的极限分布

基于渐近正态随机变量,导出随机变量函数极限分布的两个一般性理论结果.作为应用,证明了渐近正态随机变量一系列具体函数的极限分布,其中包括泊松随机变量平方根的渐近正态性,以及随机变量部分和在正则化常数是随机变量情况下的渐近正态性.     

关于任意随机变量序列的强极限定理的一个注记

主要说明两两NQD随机变量序列的一些收敛性质是任意随机变量序列的强极限定理的推论.     

Statistical inferences based on INID progressively type II censored order statistics

Suppose that the failure times of the units placed on a life-testing experiment are independent but nonidentically distributed random variables. Under progressively type II censoring scheme, distributional properties of the proposed random variables are presented and some inferences are made. Assuming that the random variables come from a proportional hazard rate model, the formulas are simplified and also the amount of Fisher information about the common parameters of this family is calculated. The results are also extended to a fixed covariates model. The performance of the proposed procedure is investigated via a real data set. Some numerical computations are also presented to study the effect of the proportionality rates in view of the Fisher information criterion. Finally, some concluding remarks are stated.     

一种考虑属性具有关联性的正态随机多属性决策方法

针对属性具有关联性的正态随机多属性决策问题,给出一种决策方法。首先,将正态随机变量形式的属性值进行规范化;然后,在考虑属性之间具有关联性的情况下,运用正态随机变量计算公式和Choquet积分计算公式,对规范化后的属性值进行集结,得到各方案的正态随机变量形式的综合评价值。进一步地,依据事先定义的正态随机变量的序关系确定规则,对各方案的综合评价值进行排序,进而确定方案的排序结果。最后,通过一个算例说明了本文给出方法的可行性和有效性。     

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Letbe a sequence of real-valued random variables and be other random variables which are independent of the form sequence. Suppose that are pairwise generalized negatively orthant dependent with heavy tails under the condition that are independent or associated, some asymptotic formulas are established.     

A note on the sum of uniform random variables

An inductive procedure is used to obtain distributions and probability densities for the sum S_n of independent, non-equally uniform random variables. Some known results are then shown to follow immediately as special cases. Under the assumption of equally uniform random variables some new formulas are obtained for probabilities and means related to S_n. Finally, some new recursive formulas involving distributions are derived.     

Nonstationary generalized Duru-Kleinert transformation of path integrals for systems of differential equations in one-dimensional space

We obtain new formulas for the transformations of Wiener path integrals corresponding to the parabolic systems of two differential equations with time-dependent coefficients in one-dimensional space. These formulas determine the transformation of the path integrals under a rheonomous-homogeneous-pointwise transformation of integration variables and the path reparameterization transformation. These formulas allow us to obtain an integral relation between the Green's functions of related systems of differential equations. We show how to obtain the generalized Shepp formula from this relation for the path integral under consideration. We derive these new formulas using the properties of random processes under phase transitions and a random change in time.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 1, pp. 17–27, October, 1996.     

Stochastic perturbation approach to the wavelet‐based analysis

The wavelet‐based decomposition of random variables and fields is proposed here in the context of application of the stochastic second order perturbation technique. A general methodology is employed for the first two probabilistic moments of a linear algebraic equations system solution, which are obtained instead of a single solution projection in the deterministic case. The perturbation approach application allows determination of the closed formulas for a wavelet decomposition of random fields. Next, these formulas are tested by symbolic projection of some elementary random field. Copyright © 2004 John Wiley & Sons, Ltd.     

Moment functions of a solution of the diffusion equation with Gaussian random coefficients

We obtain formulas for the expectation and the second moment function of the solution of the Cauchy problem for an inhomogeneous differential heat equation with two phase variables and with independent Gaussian random coefficients.     

概率论中有关计算公式的改进

通过对概率论中有关公式的研究 ,给出了全条件概率公式和二维随机变量函数的密度函数的简化计算公式 ,为其计算提供了新的方法     

Tail dependence of random variables from ARCH and heavy-tailed bilinear models

Discussed in this paper is the dependent structure in the tails of distributions of random variables from some heavy-tailed stationary nonlinear time series. One class of models discussed is the first-order autoregressive conditional heteroscedastic (ARCH) process introduced by Engle (1982). The other class is the simple first-order bilinear models driven by heavy-tailed innovations. We give some explicit formulas for the asymptotic values of conditional probabilities used for measuring the tail dependence between two random variables from these models. Our results have significant meanings in finance.     

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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.