Hausdorff dimension of the graph of the fractional Brownian sheet
Let \(\{B^{(\alpha)}(t)\}_{t\in R^d}\) be the fractional Brownian sheet with multi-index \(\alpha=(\alpha_1,\dots,\alpha_d)\), \(0<\alpha_i<1\). Kamont has shown that, with probability \(1\), the box dimension of the graph of a trajectory of this Gaussian field, over a non-degenerate cube \(Q\subset R^d\), is equal to \(d+1-\min(\alpha_1,\dots,\alpha_d)\). This paper proves that this result remains true when the box dimension is replaced by the Hausdorff dimension or the packing dimension.
scientific article; zbMATH DE number 2110192
scientific article