Hausdorff dimension of the graph of the fractional Brownian sheet
type: Item
instance of: scholarly article
title: Hausdorff dimension of the graph of the fractional Brownian sheet
zbMATH Open document ID: 1057.60033
DOI: 10.4171/RMI/394
author: Antoine Ayache
published in: Revista Matemática Iberoamericana
publication date: 2004-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39715
review text: 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.
reviewed by: Yuhu Feng
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 2110192
zbMATH Keywords: Gaussian fields
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: random wavelet series
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: packing dimension
MaRDI profile type: Publication
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OpenAlex ID: W2026762452
description: scientific article; zbMATH DE number 2110192