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The Gaussian measure of shifted balls
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  • Published: June 1994

The Gaussian measure of shifted balls

  • James Kuelbs1,
  • Wenbo V. Li2 &
  • Werner Linde3 

Probability Theory and Related Fields volume 98, pages 143–162 (1994)Cite this article

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  • 30 Citations

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Summary

Let μ be a centered Gaussian measure on a Hilbert spaceH and let\(B_R \subseteq H\) be the centered ball of radiusR>0. Fora∈H and\(\mathop {\lim }\limits_{t{\mathbf{ }} \to {\mathbf{ }}\infty } {\mathbf{ }}R(t)/t< {\mathbf{ }}||a||\), we give the exact asymptotics of μ(B R(t)+t·a) ast→∞. Also, upper and lower bounds are given when μ is defined on an arbitrary separable Banach space. Our results range from small deviation estimates to large deviation estimates.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, 53706, Madison, WI, USA

    James Kuelbs

  2. Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA

    Wenbo V. Li

  3. Sektion Mathematik, Friedrich-Schiller-Universität, 07743, Jena, Germany

    Werner Linde

Authors
  1. James Kuelbs
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  2. Wenbo V. Li
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  3. Werner Linde
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Additional information

Supported in part by NSF grant number DMS-9024961

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Kuelbs, J., Li, W.V. & Linde, W. The Gaussian measure of shifted balls. Probab. Th. Rel. Fields 98, 143–162 (1994). https://doi.org/10.1007/BF01192511

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  • Received: 02 September 1992

  • Revised: 19 August 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192511

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Mathematics Subject Classification (1991)

  • 60B05
  • 60B12
  • 60G15
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