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


DOI: 10.1007/s00440-004-0363-x

Cite this article as:
Fill, J. & Torcaso, F. Probab. Theory Relat. Fields (2004) 130: 259. doi:10.1007/s00440-004-0363-x


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:

AsymptoticsIntegrated Brownian sheetMellin transformHarmonic sumGeneralized Dirichlet seriesSmall deviationsReversion

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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