Intersections and polar functions of fractional brownian sheets |
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Authors: | Chen Zhenlong |
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Institution: | College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China |
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Abstract: | Let BH = {BH(t), t ∈ RN } be a real-valued (N, d) fractional Brownian sheet discussed. The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of BH is obtained. The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov's entropy index for BH are presented. Furthermore, it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions. A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved. |
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Keywords: | Fractional Brownian sheet polar function Hausdorff dimension intersection |
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