Asymptotic analysis via Mellin transforms for small deviations in $L^2$-norm of integrated Brownian sheets

Abstract

We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared $L^2$-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.

29 pages. See also http://www.mts.jhu.edu/~fill/ and http://www.mts.jhu.edu/~torcaso/ . Submitted for publication in September, 2003