负相协随机变量非随机和的差的精确大偏差

In this paper,we study precise large deviation for the non-random difference sum from j=1 to n_1(t) X_(1j)-sum from j=1 to n_2(t) X_(2j),where sum from j=1 to n_1(t) X_(1j) is the non-random sum of {X_(1j),j≥1} which is a sequence of negatively associated random variables with common distribution F_1(x),and sum from j=1 to n_2(t) X_(2j) is the non-random sum of {X_(2j),j≥1} which is a sequence of independent and identically distributed random variables,n_1(t) and n_2(t) are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r(n_1(t))~(p+1)|(P(∑~(n_1(t)_(j=1)X_(1j)-∑~(n_2(t)_(j=1)X_(2j)-(μ_1n_1(t)-μ_2n_2(t)x))/(n_1(t)F_1(x))-1|=0.     

负相协重尾随机变量随机和的中偏差

本文讨论了具有重尾负相协索赔的经典风险模型．通过一种改进后的大偏差技术，给出了索赔总量过程的中偏差结果：所获结果推广了独立索赔情形下的相应的结果．     

基于偏差密度模型的小波估计

讨论了带加权分布且基于分层相协随机变量的密度函数估计问题,提出了线性小波估计器,并给出该估计器的L~p(1≤p∞)风险上界.     

一类负相伴随机阵列部分和的精致大偏差

本文在一些适当的条件下得到了多风险模型中负相伴随机阵列的精致大偏差,推广了一些已知的结果,同时表明在多风险模型中负相伴结构对精致大偏差同样不具有敏感性.     

部分转移风险过程的大偏差

本文研究了部分转移风险过程的大偏差问题.利用构造指数鞅的方法,得到了部分转移风险过程的大偏差.该结果给出部分转移风险过程的一个渐近行为.     

随机变量的负超可加相依及其应用

一个随机向量Ｘ＝（Ｘ１,Ｘ２,．．．,Ｘｍ）称为负超可加相依（ＮＳＤ）,如果对每个超可加函数Х,ＥХ（Ｘ１,Ｘ２,．．．,Ｘｍ）≥ＥХ（Ｙ１,Ｙ２,．．．,Ｙｍ）,其中Ｙ１,Ｙ２,．．．,Ｙｍ相互独立且对任意ｉ,Ｙｉ＝ｄＸｉ,本文研究了ＮＳＤ的基本性质,给出了ＮＳＤ判定的三个结构 定理,并且这些定理可用来证明许多著名的多元分布具有ＮＳＤ性质,本文还给出了ＮＡＤ的许多概率不等式。     

基于负相协样本的经验过程的弱收敛

我们借助于一个Ｒｏｓｅｒｎｔｈａｌ型不等式建立了基于负相协样本经验过程的弱收敛性,同时在证明过程中我们给出了负相协随机变量的几个有用的矩不等式。     

复合二项分布下多险种风险模型的大偏差

考虑了重尾分布的多险种复合二项风险模型,在索赔额分布服从一致变化尾时,得到了其总索赔过程和总索赔盈利过程的大偏差,推广了经典复合二项风险模型的结论.     

L族END的多元部分和的精确大偏差下界

从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界.     

一类新风险过程的精细大偏差

本文针对基于进入过程的保险风险模型(LIG),讨论了当索赔额属于C族时,风险过程的精细大偏差.     

弱拓扑下的非线性随机积分和微分方程组的解

在本文中，我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理．利用这一定理，我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则．作为应用，我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理．也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果．我们的定理改进和推广了Szep，Mitchell－Smith，Cramer－Lakshmikantham，Lakshmikantham—Leela和丁的相应结果．     

Random homogenization and convergence to integrals with respect to the Rosenblatt process

This paper concerns the random fluctuation theory of a one dimensional elliptic equation with highly oscillatory random coefficient. Theoretical studies show that the rescaled random corrector converges in distribution to a stochastic integral with respect to Brownian motion when the random coefficient has short-range correlation. When the random coefficient has long-range correlation, it was shown for a large class of random processes that the random corrector converged to a stochastic integral with respect to fractional Brownian motion. In this paper, we construct a class of random coefficients for which the random corrector converges to a non-Gaussian limit. More precisely, for this class of random coefficients with long-range correlation, the properly rescaled corrector converges in distribution to a stochastic integral with respect to a Rosenblatt process.     

Fuzzy random renewal process and renewal reward process

So far, there have been several concepts about fuzzy random variables and their expected values in literature. One of the concepts defined by Liu and Liu (2003a) is that the fuzzy random variable is a measurable function from a probability space to a collection of fuzzy variables and its expected value is described as a scalar number. Based on the concepts, this paper addresses two processes—fuzzy random renewal process and fuzzy random renewal reward process. In the fuzzy random renewal process, the interarrival times are characterized as fuzzy random variables and a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process is presented. In the fuzzy random renewal reward process, both the interarrival times and rewards are depicted as fuzzy random variables and a fuzzy random renewal reward theorem on the limit value of the long-run expected reward per unit time is provided. The results obtained in this paper coincide with those in stochastic case or in fuzzy case when the fuzzy random variables degenerate to random variables or to fuzzy variables.     

The existence and uniqueness of<Emphasis Type="Italic">q</Emphasis>-process in random environment

We introduce some basic concepts such as random (sub-)transition function, q-function in random environment, g-process in random environment and some basic lemmas. For any continuous g-function in random environment, we prove that the g-process in random environment always exists, and that any g-process in random environment satisfies the random Kolmogorov backward equation and the minimal g-process in random environment always exists. When g is a continuous and conservative g-function in random environment, the necessary and sufficient conditions for the uniqueness of g-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous g-processes in random environments are considered.     

General algorithm of random solutions for random nonlinear variational inequalities in banach Spaces *

In this paper, we study a class of random nonlinear variational inequalities in Banach spaces. By applying a random minimax inequahty obtained by Tarafdar and Yuan, some existence uniqueness theorems of random solutions for the random nonhnear variational inequalities are proved. Next, by applying the random auxiliary problem technique, we suggest an innovative iterative algorithm to compute the random approximate solutions of the random nonlinear variational inequahty. Finally, the convergence criteria is also discussed     

非线性随机积分和微分方程组的解

在本文中我们首先对具有随机定义域的连续随机算子组证明了Ｄａｒｂａｏ型不动点定理．应用此定理我们给出了非线性随机Ｖｏｌｔｅｒｒａ积分方程组和非线性随机微分方程组的Ｃａｕｃｈｙ问题解的存在性准则．这些随机方程组的极值随机解的存在性和随机比较结果也被获得．我们的定理改进和推广Ｔｙａｕｇｈｎ，Ｌａｋｓｈｍｉｋａｎｔｈａｍ，Ｌａｋｓｈｍｉｋａｎｔｈａｍ－Ｌｅｅｌａ，ＤｅＢｌａｓｔ－Ｍｙｊａｋ和第一作者的相应结果．     

Random fuzzy shock models and bivariate random fuzzy exponential distribution

In this paper, a random fuzzy shock model and a random fuzzy fatal shock model are proposed. Then bivariate random fuzzy exponential distribution is derived from the random fuzzy fatal shock model. Furthermore, some properties of the bivariate random fuzzy exponential distribution are proposed. Finally, an example is given to show the application of the bivariate random fuzzy exponential distribution.     

Quenched tail estimate for the random walk in random scenery and in random layered conductance

We discuss the quenched tail estimates for the random walk in random scenery. The random walk is the symmetric nearest neighbor walk and the random scenery is assumed to be independent and identically distributed, non-negative, and has a power law tail. We identify the long time asymptotics of the upper deviation probability of the random walk in quenched random scenery, depending on the tail of scenery distribution and the amount of the deviation. The result is in turn applied to the tail estimates for a random walk in random conductance which has a layered structure.     

Random approximations and random fixed point theorems for random 1-setn-contractive non-self-maps in abstract cones

In this paper, we will prove that the random version of Fan's Theorem [6, Theorem 2] is true for a random hemicompact 1-set-contractive map defined on a closed ball, a sphere and an annulus in cones. This class of random 1-set-contractive map includes random condensing maps, random continuous semicontractive maps, random LANE maps, random nonexpansive maps and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations, improvements or stochastic versions of the recent results obtained by many authors     

随机赋范空间中算子随机范数与共鸣定理及应用

基于概率论理论基础,给出了随机赋范空间中算子的随机范数定义,在此基础上,应用逆算子定理证明了随机赋范空间中算子族的共鸣定理,它以Banach空间中的共鸣定理为特例,是Banach空间中的共鸣定理的随机化形式,随机化的共鸣定理刻划了在随机赋范空间框架下随机变量族的一致有界性.随机赋范空间中的共鸣定理将可能成为随机泛函分析与概率论的新应用工具.