POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS  

作　　者：陈振龙 李慧琼 

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

出　　处：《Acta Mathematica Scientia》2010年第3期857-872,共16页数学物理学报（B辑英文版）

基　　金：supported by the national natural foundationof China (70871104);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） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

关 键 词：Bifractional Brownian sheet polar set Hausdorff dimension packing dimen- sion capacity 

分 类 号：O211.6[理学—概率论与数理统计]