Intersections and polar functions of fractional brownian sheets

Let BH = BH (t), t∈ RN+ be a real-valued (N, d) fractional Brownian sheet with Hurst index H=(H1, …, HN). The characteristics of the polar functions for BH are 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 Hölder condition is also solved.