RESEARCH ARTICLE

Fractal and smoothness properties of space-time Gaussian models

  • Yun XUE ,
  • Yimin XIAO
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  • Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA

Received date: 07 Aug 2010

Accepted date: 01 Mar 2011

Published date: 01 Dec 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Yun XUE , Yimin XIAO . Fractal and smoothness properties of space-time Gaussian models[J]. Frontiers of Mathematics in China, 2011 , 6(6) : 1217 -1248 . DOI: 10.1007/s11464-011-0126-9

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