1 research outputs found
Functional Quantization and Entropy for Stochastic Processes
Let X be a Gaussian process and let U denote the
Strassen ball of X. A precise link between the
L^2-quantization error of X and the Kolmogorov
(metric) entropy of U in a Hilbert space setting
is established. In particular, the sharp
asymptotics of the Kolmogorov entropy problem is
derived. The condition imposed is regular
variation of the eigenvalues of the covariance
operator. Good computable quantizers for Gaussian
and diffusion processes and their numerical
efficieny are discussed.
This is joint work with G. Pagès, Université de Paris 6