POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

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

Abstract

Abstract:

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.

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

CLC Number:

60G15

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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