Rates of clustering for some Gaussian self-similar processes |
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Authors: | Victor Goodman James Kuelbs |
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Affiliation: | (1) Department of Mathematics, Indiana University, 47405 Bloomington, IN, USA;(2) Department of Mathematics, University of Wisconsin, 53706 Madison, WI, USA |
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Abstract: | Summary The analogue of Strassen's functional law of the iterated logarithm in 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 toK 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 1, was highly dependent on many special properties unavailable when dealing with other Gaussian processes.Supported in part by NSF Grant NSF-88-07121Supported in part by NSF Grant DMS-85-21586 |
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