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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Mason, D.M., Shi, Z. Small Deviations for Some Multi-Parameter Gaussian Processes. Journal of Theoretical Probability 14, 213–239 (2001). https://doi.org/10.1023/A:1007833401562
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DOI: https://doi.org/10.1023/A:1007833401562