Small Deviations for Some Multi-Parameter Gaussian Processes

David M. Mason () and Zhan Shi
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David M. Mason: University of Delaware
Zhan Shi: Université Paris VI

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 213-239

Abstract: Abstract We prove some general lower bounds for the probability that a multi-parameter Gaussian process has very small values. These results, when applied to a certain class of fractional Brownian sheets, yield the exact rate for their so-called small ball probability. We show by example how to use such results to compute the Hausdorff dimension of some exceptional sets determined by maximal increments.

Keywords: Gaussian random field; fractional Brownian sheet; small ball probability; Hausdorff dimension; exceptional set; random fractal (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1007833401562

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