如何计算可实现Fuzzy矩阵的容度

本文给出一种［ｒ（Ａ）］ｎ２步内找到Ｆｕｚｚｙ矩阵Ｂ∈　Ｌｎ×ｒ（Ａ）,使Ａ＝Ｂ⊙ＢＴ成立,从而计算出给定可实现Ｆｕｚｚｙ矩阵Ａ的容度ｒ（Ａ）的算法．     

布朗运动在（r，p）－容度意义下的下极限性质

本文证明了布朗运动在（ｒ,ｐ）－容度意义下的一些基本下极限性质．     

随机发展方程小扰动的容度大偏差原理

本文证明了随机发展方程小扰动的容度大偏差原理，所获结果改进和加强已知的结果     

布朗运动在（r，p）－容度意义下的下极限性质

本文证明了布朗运动在（ｒ，ｐ）－容度意义下的一些基本下极限性质．     

拟必然分析概述

经典的几乎必然分析研究的是随机变量和或机过程除去概率为零的集合以外的性质，容度的概念起源于电学，其严格的数学理论由Ｎ．Ｗｉｅｎｅｒ及Ｇ．Ｃｈｏｑｕｅｔ所发展，８０年代Ｐ．Ｍａｌｌｉａｖｉｎ建立了Ｗｉｅｎｅｒ空间上的非线性容度理论，拟必然分析便是研究除去零容集以外成立的性质的理论，本文概述了了这一理论的发展和现状。     

关于容度下Borel-Cantelli引理的一点注记

这个注记中我们证明了在没有两两独立假设条件下对容度的Borel-Cantelli引理,获得了容度对并事件的最优下界.这些结果推广了经典的Borel-Cantelli引理.     

扩散过程关于（r，p）－容度的大偏差

本文证明扩散过程关于（ｒ，ｐ）－容度服从大偏差原理，作为此结果的一个应用，我们证明扩散过程的拟泛函重对数律成立．     

可实现布尔矩阵的容度与无向图的团覆盖数

讨论了可实现布尔矩阵的容度问题.将可实现布尔矩阵看成是无向图,我们证明了可实现布尔矩阵的容度等于其相应无向图的团覆盖数与孤立点数之和,并给出了通过计算容度来计算团覆盖数,以及通过计算团覆盖数来计算容度的算法框架.     

关于Rn中的几何容度的刚性定理

本文研究Rⁿ中开子集的由几何容度刻画的几何性质,并证明两个刚性定理:若区域在其某一边界点处的任一尺度之下都具有相应的锥的容度,则该区域必定是具有相同立体角的锥体;若区域的任意边界点均满足如上容度条件,则该区域只能为半空间.     

反射扩散过程的极集

本文利用Ｄｉｒｉｃｈｌｅｔ型中有产在容度的结论，从几何的观点刻画了反射扩散过程的极集。     

A large deviation principle for (r,p)-capacities on the Wiener space

Summary We formulate and prove a large deviation principle for the (r, p)-capacity on an abstract Wiener space. As an application, we obtain a sharpening of Strassen's law of the iterated logarithm in terms of the capacity.     

Sobolev spaces and capacities theory on path spaces over a compact Riemannian manifold

We introduce Sobolev spaces and capacities on the path space P _{m 0} (M) over a compact Riemannian manifold M. We prove the smoothness of the Itô map and the stochastic anti-development map in the sense of stochastic calculus of variation. We establish a Sobolev norm comparison theorem and a capacity comparison theorem between the Wiener space and the path space P _{m 0} (M). Moreover, we prove the tightness of (r, p)-capacities on P _{m 0} (M), \(\), which generalises a result due to Airault-Malliavin and Sugita on the Wiener space. Finally, we extend our results to the fractional Hölder continuous path space \(\).     

混合范数条件下平移不变信号的非均匀平均采样

L~p平移不变子空间中的采样研究通常要求生成函数属于一个不依赖于p的Wiener amalgam空间,此条件因不能控制p而显得太强.本文主要讨论生成函数属于混合范数空间时,非衰减平移不变空间中的非均匀平均采样与重构.生成函数属于混合范数空间的条件弱于Wiener amalgam空间且依赖于参数p.基于混合范数空间中的一些引理,针对两种平均采样泛函建立了采样稳定性,并给出了对应的具有指数收敛的迭代重构算法.     

Hausdorff measures on the Wiener space

We construct a Hausdorff measure of finite co-dimension on the Wiener space. We then extend the Federer co-area Formula to this Wiener space for functions with the sole condition that they belong to the first Sobolev space. An explicit formula for the density of the images of the Wiener measure under such functions follows naturally from this. As a corollary, this yields a new and easy proof of the Krée-Watanabe theorem concerning the regularity of the images of the Wiener measure.     

On Lebesgue Integrability of Fourier Transforms in Amalgam Spaces

Journal of Fourier Analysis and Applications - Let f be an element of the subspace $$(L^{q},l^{p})^{\alpha }({\mathbb {R}}^d)$$ ( $$1\le q \le \alpha \le p \le 2 $$ ) of the Wiener amalgam space...     

Various topologies in the Wiener space and Lévy's stochastic area

Summary In this paper, we observe how Lévy's stochastic area looks when we see it through various topologies in the Wiener space. Our theorem implies that it is quite natural from the viewpoint of topology to define a distinct skeleton of Lévy's stochastic areaS(w) for each distinct topology in the Wiener space, or equivalently, for each distinct abstract Wiener space on which the Wiener measure andS(w) are realized. Thus we cannot determine its intrinsic skeleton in the theory of abstract Wiener spaces.     

ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W（L^p（x）, Lm^q）

In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global component is a weighted Lebesgue space Lm^q （R）. This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W （L^p（x）, Lm^q） = L^q （R）. Later we give some characterization of Wiener amalgam space W （L^p（x）, Lm^q）.In Section 3 we define the Wiener amalgam space W （FL^p（x）, Lm^q） and investigate some properties of this space, where FL^p（x） is the image of L^p（x） under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

Evaluation formulas for conditional abstract wiener integrals

In this paper we consider abstract Wiener space version of conditional Wiener integrals and establish formulas for evaluating conditional abstract Wiener integrals for various classes of functions on an abstract Wiener space. We then apply our formulas to evaluate certain Wiener integrals and conditional Wiener and Yeh-Wiener integrals     

The local times and Hausdorff measure for level sets of a Wiener sheet

In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rd-valued Wiener sheet is (r)=rN-d/2(loglog1/r)d/2 if 2N＞d. This solves the problem posed by S. J. Taylor.