随机模糊集与随机集

本文研究了三个方面的工作：一是定义了一种模糊集上的可测结构，从而定义了随机模糊集，这些定义都与论域Ｘ上的拓扑结构无关。将通常意义下的集合看成特殊模糊集得到的通常集合上的超可测结构与文（３）中的定义一致；二是给出了随机模糊集、随机集的一些等价条件；三是研究了随机模糊集、随机集的分布与其有限维落影族的关系。     

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.     

随机非线性凝聚算子方程的随机解

利用随机拓扑度理论研究随机非线性凝聚算子,在一定条件下得到随机算子方程A（w,x）=μx的随机解和随机算子不动点的存在性,所得结论减弱了已知文献中相应定理的条件．     

时间随机环境下随机游动的渐近行为

本文给出了可数状态空间中时间随机环境下随机游动的一个统一的模型 .对于最常见的情况 ,即d维最近邻域随机环境下随机游动 ,如果环境是严平稳的 ,则在一定条件下 ,该随机游动满足强大数定律和中心极限定理 .特别地 ,当环境独立同分布时 ,我们可以得到更为具体的结果 ,该结果类似于经典的随机游动的相应结论 .     

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Let be a correlated random walk in random environment. For the sub-linear regime, that is, almost surely but , we show that there is ??Let be a correlated random walk in random environment. For the sub-linear regime, that is, almost surely but , we show that there is $0s. This result characterizes the slowdown property of the walk.     

On a Class of Random Variational Inequalities on Random Sets

We study a class of random variational inequalities on random sets and give measurability, existence, and uniqueness results in a Hilbert space setting. In the special case where the random and the deterministic variables are separated, we present a discretization technique based on averaging and truncation, prove a Mosco convergence result for the feasible random set, and establish norm convergence of the approximation procedure.     

随机自反随机赋范模上的平均遍历定理(英文)

本文对随机自反随机赋范模上的几乎处处幂有界的随机线性算子证明了一个平均遍历定理,这一定理推广和改进了几个已知的重要的结果.     

一类随机环境中的随机游动

在Solomn的模型的基础上对一类随机环境中随机游动进行了讨论，并得出了一个常返性准则和一些极限性质。     

Self-Similar Random Thermodynamics

We provide a short introduction into self-similar (random) thermodynamics. It is a generalization of the classical thermodynamics to the random self-similar case. Further, as an application, we give a formula of the dimension of self-conformal random fractals.     

Random Walks in Random Media on a Cayley Tree

We present sufficient conditions for the transience of random walks with bounded jumps in random media on a Cayley tree.     

Random fuzzy renewal process

This paper attempts to discuss a random fuzzy renewal process based on random fuzzy theory. The interarrival times are characterized as nonnegative random fuzzy variables which is a more reasonable consideration in the real world. Under this setting, the rate of the random fuzzy renewal process is discussed and a random fuzzy elementary renewal theorem is presented. Furthermore, the expected value of renewals in an arbitrary interval is investigated and Blackwell’s theorem in random fuzzy sense is also established.     

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.     

Boundaries and Harmonic Functions for Random Walks with Random Transition Probabilities

The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence of measures, so that the resulting (random) Markov chains are still space homogeneous, but no longer time homogeneous. We study various notions of measure theoretical boundaries associated with this model and establish an analogue of the Poisson formula for (random) bounded harmonic functions. Under natural conditions on transition probabilities we identify these boundaries for several classes of groups with hyperbolic properties and prove the boundary triviality (i.e., the absence of non-constant random bounded harmonic functions) for groups of subexponential growth, in particular, for nilpotent groups.     

Generating a Random Signed Permutation with Random Reversals

Signed permutations form a group known as the hyperoctahedral group. We bound the rate of convergence to uniformity for a certain random walk on the hyperoctahedral group that is generated by random reversals. Specifically, we determine that O(n log n) steps are both necessary and sufficient for total variation distance and ℓ² distance to become small. This random walk arose as the result of an effort in molecular biology to model certain types of genome rearrangements.     

一类随机环境中的随机游动

研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论.     

随机集值系统解的存在定理(英文)

在Banach空间介绍一类意义更广的随机集值系统x(ω)∈F(ω,x(ω),y(ω)),y(ω)∈G(ω,x(ω),y(ω)),并且在一定条件下证明这类系统随机解的存在性,其中F和G是随机集值映射.     

Random Markov-self-similar measures

Fractals and measures are often defined in a constructive way. In this paper, we give the construction of random measures concentrated on random Markov-self-similar fractals and prove that under quite weak conditions random Markov-self-similar measures exist and satisfy certain self-similarity property.     

关于随机一致凸性

致力于随机一致凸性概念的进一步探讨．首先,通过一个特殊的层次剖分指出对任意的随机赋范模而言随机凸性模都有良好定义,从而改进了近期的文献中许多已知的结果．然后,提出并研究了一种与随机一致凸性密切相关的新性质,从一个新的角度阐述了随机一致凸性的复杂性．     

关于随机最远点

首先给出在随机赋范模中子集的随机最远点的概念．进一步,利用随机一致凸性和经典一致凸性之间的联系证明了下面的结果：令（E,｜｜·｜｜）为完备的随机一致凸的随机赋范模,S为E中几乎处处有界并在（ε, λ）一拓扑下的闭子集,则具有S中随机最远点的集合稠于E．