Abstract.
We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L2-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.
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Research supported by NSF grant DMS–0104167, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement of Research in Statistics.
Mathematics Subject Classification (2000):Primary 60G15, 41A60; secondary 60E10, 44A15, 41A27
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Fill, J., Torcaso, F. Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets. Probab. Theory Relat. Fields 130, 259–288 (2004). https://doi.org/10.1007/s00440-004-0363-x
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DOI: https://doi.org/10.1007/s00440-004-0363-x