Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

Wenbo V. Li () and Qi-Man Shao ()
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Wenbo V. Li: University of Delaware
Qi-Man Shao: University of Oregon

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 699-720

Abstract: Abstract A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.

Keywords: Gaussian process; Wiener process; fractional Brownian motion; Sobolev norm; Chung's LIL (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021675731663

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