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Large and moderate deviations for intersection local times
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  • Published: 26 November 2003

Large and moderate deviations for intersection local times

  • Xia Chen1 &
  • Wenbo V. Li2 

Probability Theory and Related Fields volume 128, pages 213–254 (2004)Cite this article

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  • 35 Citations

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Abstract.

We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L 2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and Yor (1991) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

    Xia Chen

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

    Wenbo V. Li

Authors
  1. Xia Chen
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  2. Wenbo V. Li
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Corresponding author

Correspondence to Xia Chen.

Additional information

Supported in part by NSF Grant DMS-0102238

Supported in part by NSF Grant DMS-0204513

Mathematics Subject Classification (2000): Primary: 60J55; Secondary: 60B12, 60F05, 60F10, 60F15, 60F25, 60G17, 60J65

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Chen, X., Li, W. Large and moderate deviations for intersection local times. Probab. Theory Relat. Fields 128, 213–254 (2004). https://doi.org/10.1007/s00440-003-0298-7

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  • Received: 04 November 2002

  • Revised: 02 September 2003

  • Published: 26 November 2003

  • Issue Date: February 2004

  • DOI: https://doi.org/10.1007/s00440-003-0298-7

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Keywords

  •  Brownian motion
  • Random walk
  • Intersection local times
  • Large deviation
  • The law of the iterated logarithm
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