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

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

2003-09-23

arxiv.org/abs/math/0309391v1

Mathematics

Probability

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

Scientific paper

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.

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