Small Deviations for Some Multi-Parameter Gaussian Processes |
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| Authors: | David M. Mason Zhan Shi |
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| Affiliation: | (1) Department of Food and Resource Economics, University of Delaware, 206 Townsend Hall, Newark, Delaware, 19717;(2) Laboratoire de Probabilités, Université Paris VI, 4 place Jussieu, 75252 Paris cedex 05, France |
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| 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. |
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| Keywords: | Gaussian random field fractional Brownian sheet small ball probability Hausdorff dimension exceptional set random fractal |
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