混合偏熵与关联熵

定义联系模糊性和随机性的混合集、混合偏熵与关联熵以及混合关联系数，研究了其性质，并举例说明混合关联系数在现实生活中的应用。     

Univariate Geometric Stable Laws

The paper summarizes recent advances in the theory of geometric stable (GS) distributions. The results presented include parametrizations, characterizations, mixture representations, properties, asymptotic and convergent series expansions of densities and distribution functions, moments and tail behavior, simulation, and estimation.     

Multivariate Geometric Stable Laws

The paper discusses recent advances in the theory of multivariate geometric stable (GS) distributions. The results presented include characterizations, mixture representations, properties, simulation, and estimation.     

Fuzzy集的偏熵与关联熵

在文献[1]的基础上,推广模糊熵的概念。首次定义Fuzzy集的偏熵、关联熵和关联熵系数等新概念。对其主要性质进行讨论,并与模糊散度建立联系．得到一些重要结果。     

Exact Rates of Convergence to a Stable Law

Let F be a non-lattice distribution function which lies in thedomain of attraction of a non-normal stable distribution. Exactuniform convergence rates are obtained for the convergence ofthe normalised partial sums of random variables with distributionF. Second order regular variation conditions are assumed relatedto the domain of attraction conditions.     

Isotopy Stable Dynamics Relative to Compact Invariant Sets

Let f be an orientation-preserving homeomorphism of a compactorientable manifold. Sufficient conditions are given for thepersistence of a collection of periodic points under isotopyof f relative to a compact invariant set A. Two main applicationsare described. In the first, A is the closure of a single discreteorbit of f, and f has a Smale horseshoe, all of whose periodicorbits persist; in the second, A is a minimal invariant Cantorset obtained as the limit of a sequence of nested periodic orbits,all of which are shown to persist under isotopy relative toA. 1991 Mathematics Subject Classification: 58F20, 58F15.     

稳定积分的弱收敛

令{X;X_n≥1}是一列严平稳的随机变量,且其分布F在一个α-稳定分布的吸引场,这里0α1.本文考虑∑_(i=1)~n f_n(β,i/n)(X_i)/(a_n)的弱收敛性.不同于经典意义下的随机过程弱收敛,本文将∑_(i=1)~n∫_n(β,in/)(X_i)/(a_n)看作β变化的随机元,利用点过程收敛方法得到了其弱收敛性.     

Entropy and Convergence on Compact Groups

We investigate the behaviour of the entropy of convolutions of independent random variables on compact groups. We provide an explicit exponential bound on the rate of convergence of entropy to its maximum. Equivalently, this proves convergence of the density to uniformity, in the sense of Kullback–Leibler. We prove that this convergence lies strictly between uniform convergence of densities (as investigated by Shlosman and Major), and weak convergence (the sense of the classical Ito–Kawada theorem). In fact it lies between convergence in L ¹⁺ and convergence in L ¹.     

Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

Symmetric Stable Laws and Stable-Like Jump-Diffusions

Asymptotic expansions are obtained for finite-dimensional symmetricstable distributions. They are used to prove the existence ofcontinuous transition probability densities of stable and stable-likejump-diffusions, and to construct local multiplicative asymptoticsandglobal two-sided estimates for these densities. As a consequence,the distribution of the first passage times for stable jump-diffusionsis estimated and the integral test for the limsup behaviourof their sample paths as t 0 is provided. 1991 MathematicsSubject Classification: 60E07, 60G17, 60J35, 47D07.     

Compactly Generated Relative Stable Categories

Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated by the class of finitely generated modules. Let H be a subgroup of G. It is possible to define a stable module category of G relative to H. This is also a triangulated category, but no non-trivial examples have been known where it was compactly generated. While the finitely generated modules are compact objects, they do not necessarily generate the category. We show that the relative stable category is compactly generated if the group algebra of H has finite representation type. In characteristic p, this is equivalent to the Sylow p-subgroups of H being cyclic.     

Newton Polytopes and Relative Entropy Optimization

Foundations of Computational Mathematics - Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We study the...     

QF-Proper Classes and Relative Stable Categories

A relative version of Rickard's theorem is proved, namely, if is a quasi-Frobenius proper class of short sequences in an Abelian category , then the -stable category of the category is a quotient category of the relative bounded derived category ( ). Bibliography: 20 titles.     

Relative Topological Pinsker Factors and Entropy Pairs

 A relative version of the topological m-Pinsker factor is given and its relationships with other notions of relative Pinsker factors are investigated. Relative topological Pinsker factors (of various kinds) of relative products are described. (Received 4 December 2000; in revised form 1 June 2001)     

Relative Entropy, Asymptotic Pairs and Chaos

In this paper, we prove that positive conditional entropy impliesthe existence of asymptotic pairs and scrambled sets on fibers.Moreover, we introduce the notion of conditional topologicalentropy for a subset using Bowen's definition of separated andspanning sets, and prove that the conditional topological entropyof a system relative to a factor is the supremum of conditionaltopological entropy of its scrambled sets on fibers.     

Stable Laws and Products of Positive Random Matrices

Let S be the multiplicative semigroup of q×q matrices with positive entries such that every row and every column contains a strictly positive element. Denote by (X _n ) _n≥1 a sequence of independent identically distributed random variables in S and by X ⁽ⁿ⁾=X _n ⋅⋅⋅ X ₁,  n≥1, the associated left random walk on S. We assume that (X _n ) _n≥1 satisfies the contraction property

Small Deviations of Stable Processes via Metric Entropy

Let X=(X(t)) _tT be a symmetric -stable, 0<<2, process with paths in the dual E ^* of a certain Banach space E. Then there exists a (bounded, linear) operator u from E into some L (S,) generating X in a canonical way. The aim of this paper is to compare the degree of compactness of u with the small deviation (ball) behavior of as 0. In particular, we prove that a lower bound for the metric entropy of u implies a lower bound for () under an additional assumption on E. As applications we obtain upper small deviation estimates for weighted -stable Levy motions, linear fractional -stable motions and d-dimensional -stable sheets. Our results rest upon an integral representation of L -valued operators as well as on small deviation results for Gaussian processes due to Kuelbs and Li and to the authors.