We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results can be applied to the Brownian sheet, fractional Brownian sheets whose Hurst indices are the same in all directions, and systems of linear stochastic wave equations in one spatial dimension driven by space–time white noise or colored noise.
The author wishes to thank Thomas Mountford and Yimin Xiao for stimulating discussions and helpful comments that have led to improvements in the paper.
"The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism." Bernoulli 28 (1) 277 - 306, February 2022. https://doi.org/10.3150/21-BEJ1342