61 citations · 184 across the 14 of their papers we have counts for
15 papers · 1 filter
Locally optimal Functional Quantization
Harald Luschgy, Gilles Pagès
In this note we demonstrate that locally optimal functional quantizers for probability distributions on a Banach space lying in the support of behave exactly like globally opti…
The nonexplosive solution of explosive autoregressions
Erich Häusler, Harald Luschgy
We establish several features of the stationary solution of purely explosive autoregressions of order d based on nonstandard initial values.
On stable central limit theorems for multivariate discrete-time martingales
Erich Häusler, Harald Luschgy
We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are str…
New approach to greedy vector quantization
Rancy El Nmeir, Harald Luschgy, Gilles Pagès
We extend some rate of convergence results of greedy quantization sequences already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general class of distributions sa…
Greedy vector quantization
Harald Luschgy, Gilles Pagès
We investigate the greedy version of the -optimal vector quantization problem for an -valued random vector . We show the existence of a sequence $(a_…
The local quantization behavior of absolutely continuous probabilities
Siegfried Graf, Harald Luschgy, Gilles Pagès
For a large class of absolutely continuous probabilities it is shown that, for , for -optimal -codebooks , and any Voronoi partition with respect…
Expansions for Gaussian processes and Parseval frames
Harald Luschgy, Gilles Pagès
We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are appli…
Asymptotically optimal quantization schemes for Gaussian processes
Harald Luschgy, Gilles Pagès, Benedikt Wilbertz
We describe quantization designs which lead to asymptotically and order optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a cruci…
Moment estimates for Lévy Processes
Harald Luschgy, Gilles Pagès
For real Lévy processes having no Brownian component with Blumenthal-Getoor index , the estimate $\E \sup\_{s \leq t} | X\_s - a\_p s |^p \leq C\_p t$ for e…
Distortion mismatch in the quantization of probability measures
Siegried Graf, Harald Luschgy, Gilles Pagès
We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show…
Functional quantization rate and mean regularity of processes with an application to Lévy processes
Harald Luschgy, Gilles Pagès
We investigate the connections between the mean pathwise regularity of stochastic processes and their L^r(P)-functional quantization rates as random variables taking values in some…
High-resolution product quantization for Gaussian processes under sup-norm distortion
Harald Luschgy, Gilles Pagès
We derive high-resolution upper bounds for optimal product quantization of pathwise contionuous Gaussian processes respective to the supremum norm on [0,T]^d. Moreover, we describe…
Optimal quantizers for Radon random vectors in a Banach space
Siegried Graf, Harald Luschgy, Pagès Gilles
For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\_{n,r}(X,E) = inf{(E (\min\_{a \in α} || X-a ||^r)^{1/r…
Functional quantization and metric entropy for Riemann-Liouville processes
Harald Luschgy, Gilles Pagès
We derive a high-resolution formula for the -quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We desc…
Sharp asymptotics of the functional quantization problem for Gaussian processes
Harald Luschgy, Gilles Pages
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 regula…