The Probability of Small Gaussian Ellipsoids and Associated Conditional Moments

Abstract

The problem of computing the lower tail of a Gaussian norm is considered in this paper. Based on large deviations arguments, a bound on these tails is derived which is tighter than those obtained by other methods. Conditional exponential moment bounds are also derived and as an application, $L^2$ type Onsager-Machlup functionals for diffusions are computed.