基于Schur-凸的不完全信息下的不平等性比较

不平等问题渐渐成为全世界的热点话题,不平等指标也显得越来越重要.由于在不平等度量中,数据采集需要耗费大量成本,如何减少数据采集量就能比较不平等程度,这是一个有趣的问题,目前没有找到相关文献.由于不平等度量指标与Schur-凸函数有着直接关联,该文以Schur-凸函数为基础,通过给出在变量向量中少量已知分量值的情况下,确定其变量向量优超上界和优超下界的方法,给出判断变量向量间优超关系的充分条件.利用该条件即能比较不平等程度.以Shannon熵为例,给出了所得充分条件下,不平等度量上的应用.     

ON CHOVER''''S LIL FOR THE WEIGHTED SUMS OF STABLE RANDOM VARIABLES

Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the integral test for the weighted partial sums {Σi=1naniXi,n ≥ 1}, and obtain the Chover's laws of iterated logarithm(LIL) as corollaries.     

SOME PROPERTIES OF GALTON-WATSON BRANCHING PROCESSES IN VARYING ENVIRONMENTS

This article deals with some properties of Galton-Watson branching processes in varying environments. A necessary and suffcient condition for relative recurrent state is presented, and a series of ratio limit properties of the transition probabilities are showed.     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

1IntroductionIn1981,J.E.Hutchinson[1]establishedthebasictheoryof(strictly)selfsimilarsets.Foragivenset(={S1,'',SN}ofcontractionmapsonacompleteseparableboundedmetricspaceN(X,d),thereexistsauniquecompactsetKsuchthatK=ZSi(K),andKistheclooureofi=1thesetofallfixedpointssi,,..-,iPoffillitecompositionsSi,o''oSi,(wesayKistheselfsimilarNsetwithrespectto().Illaddition,supposep1,-'tPNE(o,1)andZpi=l,thenthereexistsi=1NauuiqueBorelregularmeasurepoftotalmass1suchthatp=Zpipos;'withsuppp=Ki=1(we…     

概率空间上有限测度的维数及其分布

设（Ω，Ｆ，μ）为概率空间，ｖ为（Ω，Ｆ）上的有限测度的密度定理，并研究了ｖ的维数及维数分布的若干性质。     

稳定过程象测度的一些性质

设｛ｘｉ,ｔ∈Ｒ＾＋｝为ｄ维ａ介稳定过程,μ为Ｒ＾＋上正有限Ｂｏｒｅｌ测度,本文考虑由Ｘ产生的象测度μｘ的分形性质,得到了其Ｈａｎｓｄｏｒｆｆ上下维数,并利用维数给出了μｘｅｂｅｓｇｕｅ测度绝对连续的条件。     

MULTIFRACTAL DECOMPOSITION OF FRACTALS WITH FINITE MEMORY

The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq,^β.     

THE MULTIFRACTAL HAUSDORFF AND PACKING MEASURE OF GENERAL SIERPINSKI CARPETS

1 IntroductionThe self-affine sets include self-similar sets as their special case. Although the fractalproperties of self-similar sets are well understood, little is known about self-affine sets in general.McMullen[1] studied a class of self~affine sets called generlized Sierpinski carpets, and got theirHausdorff and box dimensions. King[2] got the singular spectrum of general Sierpinski carpets.In [3] Olsen introduced the multifratal Hausdorff ajnd packing measure. and use them tostudy th…     

重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

概率空间上的Packing维数

设｛Ｘｎ，ｎ≥１｝是定义在概率空间（Ω，°Ｆ，μ）上的具有有限状态空间的随机过程，ＢΩ．讨论了Ｂ的填充维数的有关性质，并得到了一类与马氏链有关的子集的维数结果