随机区域函数及其应用

本文建立了随机区域、随机区域函数的一些基本理论,由这些概念出发,通过随机区域的随机区域函数的随机稳定点的存在性,建立了任一随机区域的随机稳定中心存在的必要充分条件。     

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.     

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.     

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.     

Random solution of random multivalued operator inclusions

Sufficient conditions for a random solution of random operator inclusions involving random multivalued operators satisfying a general contractive condition are obtained. A simultaneous random solution of the system of two random operator inclusions is also derived.     

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.     

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.     

随机积分和微分方程在弱拓扑下解的存在性和比较结果*

在本文中,我们对非线性随机Volterra积分方程在Banach空间的弱拓扑下的随机解证明了几个存在定理.然后作为应用,我们得到了随机微分方程的弱随机解的存在定理.还得到了这些随机方程的极值随机解的存在性和随机比较定理.我们的定理改进和推广了[4,5,10,11,12]中的相应结果.     

Random fixed point theorems for Caristi type random operators

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.     

Random Mann iteration scheme

In the present note, a random iteration is constructed and it is proved that if the iteration is convergent, it will converge to a random fixed point of a random operator in Hilbert spaces provided that the random operator satisfies a certain contractive inequality. The iteration is a random version of Mann iteration.     

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     

Generalized random linear operators on a Hilbert space

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.     

Tubular recurrence

We introduce the directed-edge-reinforced random walk and prove that the process is equivalent to a random walk in random environment. Using Oseledec"s multiplicative ergodic theorem, we obtain recurrence and transience criteria for random walks in random environment on graphs with a certain linear structure and apply them to directed-edge-reinforced random walks. This revised version was published online in August 2006 with corrections to the Cover Date.     

Random duality

The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.     

A random walk with a branching system in random environments

We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.     

随机广义集值隐拟补问题

引入和研究一类随机广义集值隐拟补问题,构造了一个逼近问题解的随机迭代算法.在一定条件下,我们证明了这类问题解的存在性以及由随机算法所产生的序列的收敛性.