检索结果-南通市图书馆

UNIFORM packing dimension RESULTS FOR MULTIPARAMETER STABLE PROCESSES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2007年第1期27卷 1-10页

作者：钟玉泉胡迪鹤 Institute of Applied Mathematics Academia Sinica School of Mathematics Wuhan University

In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable （N, d, α）-process and αN ≤ d, then the following holds with probability 1 Dim Z（E）=α Dim E for any Borel setE ∈B（R ＋^N）, where Z（E）={x：E←t∈E,Z（t）=x}, Dim （E） denotes the packing dimension of E.

关键词：（N d α）-stable process stopping time Kolmogorov upper index packing dimension

packing dimension of generalized Moran sets

在线全文

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 1996年第2期 22-26页

作者：华苏李文侠

The packing dimeasion of generalized Moran sets is given.

关键词： generalized Moran set packing dimension open set condition.

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL dimensionS

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2023年第6期43卷 2483-2492页

作者：刘佳石赛赛张远 Institute of Statistics and Applied Mathematics Anhui University of Finance and Econo Bengbu233030China

In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].

关键词： Hausdorff dimension packing dimension graph of function product of functions

Moduli of Continuity of a Class of N-parameter Gaussian Processes and Their Fast Points

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2008年第6期24卷 901-910页

作者： Zheng Yan LIN Zong Mao CHENG Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China Institute of Applied Mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou 310018 P. R. China

We study the moduli of continuity of a class of N-parameter Gaussian processes and get some results on＇the packing dimension of the set of their fast points.

关键词： N-parameter Gaussian process modulus of continuity limsup random fractal packing dimension

Polar Functions of Multiparameter Bifractional Brownian Sheets

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2009年第2期25卷 255-272页

作者： Zhen-long Chen College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China

Let B^H,K ：（B^H,K（t）, t ∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,..., HN） ∈ （0, 1）^N and K = （K1,..., KN）∈ （0, 1]^N. The characteristics of the polar functions for B^H,K are investigated. The relationship between the class of continuous functions satisfying the Lipschitz condition and the class of polar-functions of B^H,K is presented. The Hausdorff dimension of the fixed points and an inequality concerning the Kolmogorov＇s entropy index for B^H,K are obtained. A question proposed by LeGall about the existence of no-polar, continuous functions statisfying the Holder condition is also solved.

关键词： Bifractional Brownian sheet polar function Hausdorff dimension packing dimension capacity

Polar Functions and Intersections of the Random String Processes

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2012年第10期28卷 2067-2088页

作者： Zhen Long CHEN School of Statistics and Mathematics Zhejiang Gongshang University

Let {us （x）： s 〉 0, x ∈ JR} be a random string taking values in ]Rd. The main goal of this paper is to discuss the characteristics of the polar functions of {us （x）： s ≥ 0, x ∈ JR}. The relationship between a class of continuous functions satisfying the HSlder condition and a class of polar-functions of {us（x）： s 〉 0, x ∈ R} is presented. The Hausdorff and packing dimensions of the set that the string intersects a given non-polar continuous function are determined. The upper and lower bounds are obtained for the probability that the string intersects a given function in terms of respectively Hausdorff measure and capacity.

关键词： Random string process stationary pinned string polar function Hausdorff dimension packing dimension capacity

Hitting Probabilities and Fractal dimensions of Multiparameter Multifractional Brownian Motion

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2013年第9期29卷 1723-1742页

作者： Zhen Long CHEN School of Statistics and Mathematics Zhejiang Gongshang University

The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.

关键词： Multifractional Brownian motion hitting probability inverse image level set Hausdorff dimension packing dimension

On Multifractal of Cantor Dust

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2009年第7期25卷 1175-1182页

作者： In-Soo BAEK Department of Mathematics Pusan University of Foreign Studies

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.

关键词： Cantor set Hansdorff dimension packing dimension quasi-self-similar measure local dimension

Polar Sets and Relative dimension for Generalized Brownian Sheet

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2007年第4期23卷 579-592页

作者： Hui-qiong Li Zhen-long Chenu College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310035 China

Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is also proved that if 2N ≤αd, then for any compact set E ∩→ R〉^N,d-2/α Dim E≤inf{dim F：F∈B（R^d）,P{W^～（E）∩F≠0}〉0}≤d-2/βDimE,and if 2N〉αd, then for any compact set F∪→R^d／packing dimension,α/2（d-DimF）≤inf{dimE：E∈B（R〉^N）,P{W^～（E）∩F≠0}〉0}≤β/2（d-DimF）,where B（R^d） and B（R〉^N） denote the Borel σ-algebra in R^d and in R〉^N respectively, dim and Dim are Hausdorff dimension and packing dimension respectively.

关键词： Generalized Brownian sheet polar set Hausdorff dimension packing dimension