Asymptotic behavior of the distortion-rate function for Gaussian processes in Banach spaces
Let \(\mu\) be a Gaussian measure on a separable Banach space. The author proves that the logarithmic small ball probabilities of \(\mu\) are tightly related to some moment generating functions. Based upon this link a new lower bound for the distortion-rate function against the small ball function is derived. This allows to use results of the theory of small ball probabilities to deduce lower bounds for the distortion-rate function. As application one gets several sharp weak asymptotics for this rate function.
scientific article; zbMATH DE number 5009824
scientific article