DIMENSION OF POLAR SETS FOR BROWNIAN SHEET

• Published in: Acta mathematica scientia Vol. 23; no. 4; pp. 549 - 560
• Main Author: 陈振龙 刘三阳
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2003; Department of Applied Mathematics, Xidian University, Xi'an, 710071, China; Department of Mathematics, Yangtze University, Jingzhou, 434104, China%Department of Applied Mathematics, Xidian University, Xi'an, 710071, China
• Subjects: 60G10; Brownian Sheet; Brown片; Hausdorff dimension; Hausdorff维数; packing dimension; polar set; 充分条件; 填充维数; 随机过程; polar set; Hausdorff dimension; 60G10; packing dimension; Brownian Sheet; Hansdorff dimension
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(17)30499-X

Let W={W(t);t ∈ R^N+} be the d-dlmensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F 包含于 R^d \ {0} to be a polar set for W are proved. It is also proved that if 2N ≤ d, then for any compact set E 包含于 R^N>, inf(dimF : F ∈ B(R^d), P{W(E) ∩ F ≠ Φ }> 0} = d - 2DimE, and if 2N > d, then for any compact set F 包含于 R^d\{0}, inf{dimE : E ∈ B(R^N>),p{W(E) ∩ F ≠Φ} > 0}= d/2 - DimF\2， where B(R^d) and B(R^N>) denote the Borel σ-algebra in R^d and R^N> respectively, and dim and Dim are Hausdorff dimension and Packing dimension respectively.