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Polar sets of fractional Brownian sheets

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Abstract

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.

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Authors and Affiliations

  1. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310035, China

    Zhenlong Chen

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  1. Zhenlong Chen
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Correspondence to Zhenlong Chen.

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Research supported by the National Natural Foundation of China (10471148), the Sci-tech Innovation Item for Excellent Young and Middle-Aged University Teachers of Educational Department of Hubei (200316).

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Chen, Z. Polar sets of fractional Brownian sheets. Metrika 66, 173–196 (2007). https://doi.org/10.1007/s00184-006-0104-5

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  • DOI: https://doi.org/10.1007/s00184-006-0104-5

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