Summary
Let μ be a centered Gaussian measure on a Hilbert spaceH and let\(B_R \subseteq H\) be the centered ball of radiusR>0. Fora∈H and\(\mathop {\lim }\limits_{t{\mathbf{ }} \to {\mathbf{ }}\infty } {\mathbf{ }}R(t)/t< {\mathbf{ }}||a||\), we give the exact asymptotics of μ(B R(t)+t·a) ast→∞. Also, upper and lower bounds are given when μ is defined on an arbitrary separable Banach space. Our results range from small deviation estimates to large deviation estimates.
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Supported in part by NSF grant number DMS-9024961