## Small ball probabilities around random centers of Gaussian measures and applications to quantization

 Title Small ball probabilities around random centers of Gaussian measures and applications to quantization Publication Type Journal Article Year of Publication 2003 Authors Steffen Dereich Journal J. Theor. Probab. Volume 16(2) Pagination 427-449 Keywords Gaussian process, quantization, small ball probabilites for random centers Abstract Let be a centered Gaussian measure on a separable Hilbert space . We are concerned with the logarithmic small ball probabilities around a -distributed center . It turns out that the asymptotic behavior of is a.s. equivalent to that of a deterministic function . These new insights will be used to derive the precise asymptotics of a random quantization problem which was introduced in a former article by Dereich, Fehringer, Matoussi, and Scheutzow [8].