Siegfried Graf
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Siegfried Graf has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Gilles Pagès
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France
2 shared publications - Harald Luschgy
FB IV, Mathematics University of Trier Trier Germany
2 shared publications
Latest Publications
- 22 June 2010
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 150 (1) , 167-191
Fractal functional quantization of mean-regular stochastic processes
We investigate the functional quantization problem for stochastic processes with respect to Lp(IRd, μ)-norms, where μ is a fractal measure namely, μ is self-similar or a homogeneous Cantor measure. The derived functional quantization upper rate bounds are universal depending only on the mean-regularity index of the process and the quantization dimension of μ and as universal rates they are optimal. Furthermore, for arbitrary Borel probability measures μ we establish a (nonconstructive) link between the quantization errors of μ and the functional quantization errors of the process in the space Lp(IRd, μ).
- 22 June 2010
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 150 (1) , 167-191
Fractal functional quantization of mean-regular stochastic processes
We investigate the functional quantization problem for stochastic processes with respect to Lp(IRd, μ)-norms, where μ is a fractal measure namely, μ is self-similar or a homogeneous Cantor measure. The derived functional quantization upper rate bounds are universal depending only on the mean-regularity index of the process and the quantization dimension of μ and as universal rates they are optimal. Furthermore, for arbitrary Borel probability measures μ we establish a (nonconstructive) link between the quantization errors of μ and the functional quantization errors of the process in the space Lp(IRd, μ).
- Open Access
- 23 January 2008
- Published by EDP Sciences in ESAIM: Probability and Statistics
- Vol. 12, 127-153
Distortion mismatch in the quantization of probability measures
We elucidate the asymptotics of the Ls -quantization error induced by a sequence of Lr -optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
- 23 January 2008
- Published by EDP Sciences in ESAIM: Probability and Statistics
- Vol. 12, 127-153
Open AccessDistortion mismatch in the quantization of probability measures
We elucidate the asymptotics of the Ls -quantization error induced by a sequence of Lr -optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.