I read in this paper that the fractal dimension of Gaussian white noise is infinite. The paper does not prove it nor give a reference to support it. I failed to find a reference from online searching.
Could someone please explain to me why fractal dimension of Gaussian white noise is infinite? Is Hausdorff dimension infinite too?
I am not sure which definition of Gaussian white noise is appropriate here. I would like to see if this holds for the usual definition of a Gaussian process with constant power spectral density.
Thanks a lot.