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

James Allen Fill; Fred Torcaso

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

James Allen Fill·Fred Torcaso

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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.

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James Allen Fill, Fred Torcaso. 2003-09-23. Asymptotic analysis via Mellin transforms for small deviations in $L^2$-norm of integrated Brownian sheets. https://arxiv.org/abs/math/0309391

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