Uniform dimension results for Gaussian random fields
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- Wu, D. & Xiao, Y. Sci. China Ser. A-Math. (2009) 52: 1478. doi:10.1007/s11425-009-0103-x
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When X is an (N, d)-Gaussian random field as in (1), where X1,...,Xd are independent copies of a real valued, centered Gaussian random field X0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet.