Polar sets of multiparameter bifractional Brownian sheets

Abstract

Let B H , K = { B H , K ( t ) , t ∈ ℝ + N } be an ( N,d)-bifractional Brownian sheet with Hurst indices H = ( H 1, …, H N ) ∈ (0,1) N and K = ( K 1, …, 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.