The Gaussian measure of shifted balls (Q1326276)

Let \(\mu\) be a centered Gaussian measure on a Hilbert space \(H\) and let \(B_ R\subseteq H\) be the centered ball of radius \(R>0\). For \(a \in H\) and \(\varlimsup_{t \to \infty} R(t)/t<\| a \|\), we give the exact asymptotics of \(\mu (B_{R(t)}+t \cdot a)\) as \(t \to \infty\). Also, upper and lower bounds are given when \(\mu\) is defined on an arbitrary separable Banach space. Our results range from small deviation estimates to large deviation estimates.