Probability Theory and Related Fields

, Volume 130, Issue 2, pp 259–288

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

Article

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.

Key words and phrases:

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Applied Mathematics and StatisticsThe Johns Hopkins UniversityBaltimoreUSA

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