Functional quantization and small balls probabilities for Gaussian processes

TitleFunctional quantization and small balls probabilities for Gaussian processes
Publication TypeJournal Article
Year of Publication2003
AuthorsSiegfried Graf, Harald Luschgy, and Gilles Pagès
JournalJournal of Theoretical Probability
Volume16(4)
Start Page1047-1062
Abstract

The sharp asymptotics for the $ L^2 $-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.