Gaussian random particles with flexible Hausdorff dimension

Linda V. Hansen, Thordis L. Thorarinsdottir, Evgeni Ovcharov, Tilmann Gneiting, Donald Richards

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

Original languageEnglish (US)
Pages (from-to)307-327
Number of pages21
JournalAdvances in Applied Probability
Volume47
Issue number2
DOIs
StatePublished - Jun 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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