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Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets
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  • Published: 05 July 2004

Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets

  • James Allen Fill1 &
  • Fred Torcaso1 

Probability Theory and Related Fields volume 130, pages 259–288 (2004)Cite this article

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  • 18 Citations

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Abstract.

We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L2-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, 21218-2682, USA

    James Allen Fill & Fred Torcaso

Authors
  1. James Allen Fill
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  2. Fred Torcaso
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Corresponding author

Correspondence to James Allen Fill.

Additional information

Research supported by NSF grant DMS–0104167, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement of Research in Statistics.

Mathematics Subject Classification (2000):Primary 60G15, 41A60; secondary 60E10, 44A15, 41A27

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Fill, J., Torcaso, F. Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets. Probab. Theory Relat. Fields 130, 259–288 (2004). https://doi.org/10.1007/s00440-004-0363-x

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  • Received: 27 October 2003

  • Revised: 15 March 2003

  • Published: 05 July 2004

  • Issue Date: October 2004

  • DOI: https://doi.org/10.1007/s00440-004-0363-x

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Key words and phrases:

  • Asymptotics
  • Integrated Brownian sheet
  • Mellin transform
  • Harmonic sum
  • Generalized Dirichlet series
  • Small deviations
  • Reversion
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