Gaussian measure of large balls in a Hilbert space

Abstract

Let P be a zero mean Gaussian measure in a Hilbert space. The asymptotic behavior of P { ‖ x − b ‖ 2 > ε } P\{ {\left \| {x - b} \right \|^2} > \varepsilon \} as ε → ∞ \varepsilon \to \infty is studied in this note.