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Rates of clustering for some Gaussian self-similar processes
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  • Published: March 1991

Rates of clustering for some Gaussian self-similar processes

  • Victor Goodman1 &
  • James Kuelbs2 

Probability Theory and Related Fields volume 88, pages 47–75 (1991)Cite this article

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 ℝ1, was highly dependent on many special properties unavailable when dealing with other Gaussian processes.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Victor Goodman

  2. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    James Kuelbs

Authors
  1. Victor Goodman
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  2. James Kuelbs
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Additional information

Supported in part by NSF Grant NSF-88-07121

Supported in part by NSF Grant DMS-85-21586

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Cite this article

Goodman, V., Kuelbs, J. Rates of clustering for some Gaussian self-similar processes. Probab. Th. Rel. Fields 88, 47–75 (1991). https://doi.org/10.1007/BF01193582

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  • Received: 12 December 1989

  • Revised: 26 June 1990

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01193582

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Special Property
  • Mathematical Biology
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