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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68656We 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, 2003Probability60G15, 41A60 (primary); 60E10, 44A15, 41A27 (secondary)Asymptotic analysis via Mellin transforms for small deviations in $L^2$-norm of integrated Brownian sheetstext