GAUSSIAN RANDOM PARTICLES WITH FLEXIBLE HAUSDORFF DIMENSION

被引：0

作者：

Hansen, Linda V. ^{[1
]}

Thorarinsdotiir, Thordis L. ^{[2
]}

Ovcharov, Evgeni ^{[3
]}

Gneiting, Tilmann ^{[3
,4
]}

Richards, Donald ^{[5
]}

机构：

[1] Varde Coll, DK-6800 Varde, Denmark

[2] Norwegian Comp Ctr, Oslo, Norway

[3] Heidelberg Inst Theoret Studies, Heidelberg, Germany

[4] Karlsruhe Inst Technol, D-76021 Karlsruhe, Germany

[5] Penn State Univ, University Pk, PA 16802 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2015年 / 47卷 / 02期

基金：

美国国家科学基金会;

关键词：

Celestial body; correlation function; fractal dimension; Levy basis; random field on a sphere; simulation of star-shaped random set; POSITIVE-DEFINITE FUNCTIONS; STOCHASTIC-PROCESSES; TOPOGRAPHY; MODELS; VENUS; EARTH;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：307 / 327

页数：21

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