Fractal and smoothness properties of space-time Gaussian models

doi:10.1007/s11464-011-0126-9

Front Math Chin

2011, Vol. 6

Issue (6) : 1217-1248 https://doi.org/10.1007/s11464-011-0126-9

RESEARCH ARTICLE

Fractal and smoothness properties of space-time Gaussian models

Yun XUE, Yimin XIAO(

)

Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA

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Abstract

Spatio-temporal models are widely used for inference in statistics and many applied areas. In such contexts, interests are often in the fractal nature of the sample surfaces and in the rate of change of the spatial surface at a given location in a given direction. In this paper, we apply the theory of Yaglom (1957) to construct a large class of space-time Gaussian models with stationary increments, establish bounds on the prediction errors, and determine the smoothness properties and fractal properties of this class of Gaussian models. Our results can be applied directly to analyze the stationary spacetime models introduced by Cressie and Huang (1999), Gneiting (2002), and Stein (2005), respectively.

Keywords Space-time model anisotropic Gaussian field prediction error mean square differentiability sample path differentiability Hausdorff dimension

Corresponding Author(s): XIAO Yimin,Email:xiao@stt.msu.edu

Issue Date: 01 December 2011

Cite this article:

Yun XUE,Yimin XIAO. Fractal and smoothness properties of space-time Gaussian models[J]. Front Math Chin, 2011, 6(6): 1217-1248.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0126-9
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I6/1217

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