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Publications
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"The quantization of the Cantor distribution",
Math. Nachrichten, vol. 183, pp. 113-133, 1997.
Abstract
Foundations of quantization for probability distributions,
, Secaucus, NJ, USA, Springer-Verlag New York, Inc., 2000.
Abstract
"Asymptotics of the quantization errors for self-similar probabilities",
Real Analysis Exchange 26, vol. 26(2), pp. 795-810, 2001.
"The quantization dimension of self-similar probabilities",
Math. Nachrichten, vol. 241, pp. 103-109 , 2002.
"Rates of convergence for the empirical quantization error",
Ann. Probab., vol. 30, pp. 874- 897, 2002.
"Functional quantization of Gaussian processes",
Journal of Functional Analysis, vol. 196, no. 2: Academic Press, pp. 486–531, December, 2002.
Abstract
"Functional quantization and small balls probabilities for Gaussian processes",
Journal of Theoretical Probability, vol. 16(4), 2003.
Abstract
"Quantization for probability measures with respect to the geometric mean error",
Math. Proc. Cambridge Phil. Soc., vol. 136, pp. 687-717, 2004.
Sharp asymptotics of the functional quantization problem for Gaussian processes,
, vol. 32, no. 2, 2004.
Abstract
"Sharp asymptotics of the Kolmogorov entropy for Gaussian measures",
Journal of Functional Analysis, vol. 212, no. 1, pp. 89 - 120, 2004.
Abstract
"Entropy-constrained functional quantization of Gaussian measures",
Proceedings AMS, vol. 133, pp. 3403-3409 , 2005.
Abstract
"The point density measure in the quantization of self-similar probabilities",
Math. Proc. Cambridge Phil. Soc. , vol. 138, pp. 513-531, 2005.
"Functional quantization of a class of Brownian diffusions: a constructive approach",
Stochastic Processes and their Applications, vol. 116, no. 2, pp. 310 - 336, 2006.
Abstract
"Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions",
Journal of Mathematical Analysis and Applications, vol. 318, no. 2, pp. 507 - 516, 2006.
Abstract
"Optimal quantizers for Radon random vectors in a Banach space",
J. Approx. Theory, vol. 144, no. 1, Orlando, FL, USA, Academic Press, Inc., pp. 27–53, 2007.
Abstract
"Construction of optimal quantizers for Gaussian measures on Banach spaces",
Mathematik: Universität Trier, 2008.
Abstract
"Functional quantization rate and mean pathwise regularity of processes with an application to Lévy processes",
Annals of Applied Probability, vol. 18, pp. 427-469, 2008.
Abstract
"Quantization for probability measures in the Prokhorov metric",
Theory Probab. Appl., vol. 53, pp. 216-241, 2009.
Abstract
"Asymptotically optimal quantization schemes for Gaussian processes",
ESAIM: PS, vol. 14, pp. 93 - 116, 2010.
Abstract
"A constructive sharp approach to functional quantization of stochastic processes",
Journal of Applied Mathematics, vol. 2010, 2010.
Abstract
Download: Constructive functional quantization.pdf (1.03 MB)
"Fractal functional quantization of mean-regular stochastic processes",
Mathematical Proceedings of the Cambridge Philosophical Society, 2010.
Abstract