Abstract
Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed. Under certain mild conditions, we determine the exact Hausdorff measure function for the range $$X([0,1]^N)$$ . Our result extends those in Talagrand (Ann Probab 23:767–775, 1995) for fractional Brownian motion and Luan and Xiao (J Fourier Anal Appl 18:118–145, 2012) for time-anisotropic and space-isotropic Gaussian random fields.
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