Polar Functions of Multiparameter Bifractional Brownian Sheets  

作　　者：Zhen-long Chen 

机构地区：[1]College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第2期255-272,共18页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.70471071);the Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University).

摘　　要：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.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 

分 类 号：O211.62[理学—概率论与数理统计] TP13[理学—数学]