 Local correlation dimension of multidimensional stochastic processZouhaier Dhifaoui and Jean-Marc Bardet Statistics & Probability Letters, 2022, vol. 181, issue C Abstract: The computation of the local correlation dimension is a way for estimating the Hausdorff dimension of the image of multidimensional stochastic processes. It can be obtained from the asymptotic behavior of the self-intersection occupation measure around zero. In this paper, we replace the usual indicator function of the occupation measure by a Gaussian kernel. Hence, we obtain the consistency of the local correlation dimension for multivariate fractional Brownian motion. On the other hand, we show that any used norms on Rd give the same asymptotic behavior of the occupation measure. The use of a numerical procedure based on log−log least square estimator and Monte-Carlo experiments confirm the theoretical results and provide an efficient way of estimation of the Hausdorff dimension. In addition, we show that our proposed estimation method performs the univariate one on the estimation of the Hausdorff dimension. Keywords: Occupation measure; Hausdorff dimension; Local correlation dimension; Gaussian kernel correlation integral; Semi-parametric estimation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002248 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2021.109262 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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