Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Lan, Xiaohong¹  Marinucci, Domenico²  Xiao, Yimin³ 

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230061, Anhui, Peoples R China

[2] Univ Roma Tor Vergata, Dept Math, Via Ric Sci 1, I-00133 Rome, Italy

[3] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

关键词: Spherical Gaussian fields;    Strong local nondeterminism;    Uniform modulus of continuity;    Spherical wavelets;   

DOI  :  10.1016/j.spa.2017.07.008

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with sample path properties of isotropic spherical Gaussian fields on S-2. In particular, we establish the property of strong local nondeterminism of an isotropic spherical Gaussian field based on the high-frequency behaviour of its angular power spectrum; we then exploit this result to establish an exact uniform modulus of continuity for its sample paths. We also discuss the range of values of the spectral index for which the sample functions exhibit fractal or smooth behaviour. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free