Asymptotic analysis via Mellin transforms for small deviations in $L^2$-norm of integrated Brownian sheets
Probability
2007-05-23 v1
Abstract
We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared -norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.
Keywords
Cite
@article{arxiv.math/0309391,
title = {Asymptotic analysis via Mellin transforms for small deviations in $L^2$-norm of integrated Brownian sheets},
author = {James Allen Fill and Fred Torcaso},
journal= {arXiv preprint arXiv:math/0309391},
year = {2007}
}
Comments
29 pages. See also http://www.mts.jhu.edu/~fill/ and http://www.mts.jhu.edu/~torcaso/ . Submitted for publication in September, 2003