Functional quantization of Gaussian processes
نویسندگان
چکیده
منابع مشابه
Asymptotically optimal quantization schemes for Gaussian processes ∗
We describe quantization designs which lead to asymptotically and order optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensi...
متن کاملSHARP ASYMPTOTICS OF THE FUNCTIONAL QUANTIZATION PROBLEM FOR GAUSSIAN PROCESSES By Harald Luschgy and Gilles Pagès
The sharp asymptotics for the L 2-quantization errors of Gaus-sian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues. 1. Introduction. The quantization of probability distributions is an old story which starts in the late 1940s. It has been conceived in order to drastically cut down the storage of sig...
متن کاملThe Rate of Entropy for Gaussian Processes
In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...
متن کاملAsymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes
Distribution preserving quantization (DPQ) has been proposed as a lossy coding tool that yields superior quality over conventional quantization, when applied to perceptually relevant signals. DPQ aims at the optimal rate-distortion trade-off, subject to preserving the source probability distribution. In this article we investigate the optimal DPQ for stationary Gaussian processes and the mean s...
متن کاملGaussian Processes for Functional-Coefficient Autoregressive Models
This work is concerned with nonlinear time series models and, in particular, with nonparametric models for the dynamics of the mean of the time series. We build on the functional-coefficient autoregressive (FAR) model of Chen and Tsay (1993) which is a generalization of the autoregressive (AR) model where the coefficients are varying and are given by functions of the lagged values of the series...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2002
ISSN: 0022-1236
DOI: 10.1016/s0022-1236(02)00010-1