POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

doi:10.1016/S0252-9602(10)60084-7

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 857-872.doi: 10.1016/S0252-9602(10)60084-7

POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

陈振龙, 李慧琼

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

收稿日期:2007-10-08 修回日期:2008-01-27 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
Research supported by the national natural foundation of China (70871104), the key research base for humanities and social sciences of Zhejiang Provincial high education talents (Statistics of Zhejiang Gongshang University)

POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

CHEN Zhen-Long, LI Hui-Qiong

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received:2007-10-08 Revised:2008-01-27 Online:2010-05-20 Published:2010-05-20
Supported by:
Research supported by the national natural foundation of China (70871104), the key research base for humanities and social sciences of Zhejiang Provincial high education talents (Statistics of Zhejiang Gongshang University)

摘要/Abstract

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,…, H_N) ∈ (0, 1)^N and K=(K₁, …, K_N) ∈ (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 dimension, capacity

Abstract:

Key words: Bifractional Brownian sheet, polar set, Hausdorff dimension, packing dimension, capacity

中图分类号:

60G15

陈振龙, 李慧琼. POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS[J]. 数学物理学报(英文版), 2010, 30(3): 857-872.

CHEN Zhen-Long, LI Hui-Qiong. POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS[J]. Acta mathematica scientia,Series B, 2010, 30(3): 857-872.

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POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

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