Rates of clustering for some Gaussian self-similar processes
The analogue of Strassen's functional law of the iterated logarithm is known for many Gaussian processes which have suitable scaling properties, and here we establish rates at which this convergence takes place. We provide a new proof of the best upper bound for the convergence to \({\mathcal K}\) by suitably normalized Brownian motion, and then continue with this method to get similar bounds for the Brownian sheet and other self- similar Gaussian processes. The previous method, which produced these results for Brownian motion in \({\mathbb{R}}^ 1\), was highly dependent on many special properties unavailable when dealing with other Gaussian processes.
functional law of the iterated logarithm
scientific article; zbMATH DE number 4138862