On the Link Between Small Ball Probabilities and the Quantization Problem for Gaussian Measures on Banach Spaces

66 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Functional quantization rate and mean regularity of processes with an application to Lévy processes (2006, background): “For Gaussian processes, an important connection with the small ball probability problem has been made (see [6, 14]).”
Sharp asymptotics of the functional quantization problem for Gaussian processes (2004, background): “For every n ∈ N , c ∈ (0 , 1), we have Dereich, Fehringer, Matoussi and Scheutzow (2003) or Graf, Luschgy and Pag`es (2003)].”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “In the case of Gaussian measures, upper bounds and lower bounds of the quantization error can be related to lower and upper bounds for small ball probabilities respectively [28], and a converse relationship was obtained in [34].”
Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance (2011, unknown): “It is known that the small ball function has deep links with the covering numbers of the unit ball of H , see e.g. Kuelbs-Li [19] and Li-Linde [22], as well as with the approximation of µ by measures with finite support in Wasserstein distance (the quantization or optimal quantization problem), see ”
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance (2011, background): “The couple (E,μ) is called a (separable) Gaussian–Banach space.”