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Polar sets of fractional Brownian sheets. (English) Zbl 1433.60019

Summary: The properties of the polar sets are discussed for a real-valued \((N,d)\)-fractional Brownian sheet with Hurst index. Sufficient conditions and necessary conditions for a compact set to be polar for the fractional Brownian sheet are proved. The infimum of Hausdorff dimensions of its polar sets are also obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

MSC:

60G15 Gaussian processes
28A80 Fractals
60J45 Probabilistic potential theory
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