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Publications
"An optimal Markovian quantization algorithm for multidimensional stochastic control problems",
Stochastics and Dynamics, vol. 4(4), pp. 501-545, 2004.
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
"Error analysis of the quantization algorithm for obstacle problems",
Stochastic Processes & Their Applications, vol. 106(1), 2003.
Abstract
"First order schemes in the numerical quantization method",
Mathematical Finance, vol. 13, issue 1, pp. 1-16, 2003.
Abstract
Download: First Order Schmes.pdf (218.51 KB)
"Functional quantization and small balls probabilities for Gaussian processes",
Journal of Theoretical Probability, vol. 16(4), 2003.
Abstract
"On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces",
Journal of Theoretical Probability, vol. 16(1), 2003.
Abstract
"Optimal quadratic quantization for numerics: the Gaussian case",
Monte Carlo Methods and Applications, vol. 9, pp. 135–166, 2003.
Abstract
Download: Gaussian Case.pdf (563.34 KB)
"Small ball probabilities around random centers of Gaussian measures and applications to quantization",
J. Theor. Probab., vol. 16(2), pp. 427-449, 2003.
Abstract
"Functional quantization of Gaussian processes",
Journal of Functional Analysis, vol. 196, no. 2: Academic Press, pp. 486–531, December, 2002.
Abstract
"Asymptotics of optimal quantizers for some scalar distributions",
J. Comput. Appl. Math., vol. 146, no. 2, Amsterdam, The Netherlands, The Netherlands, Elsevier Science Publishers B. V., pp. 253–275, 2002.
Abstract
"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.
"Asymptotics of the quantization errors for self-similar probabilities",
Real Analysis Exchange 26, vol. 26(2), pp. 795-810, 2001.
"A quantization algorithm for solving multidimensional optimal stopping problems, preprint",
University de Paris VI, pp. 1003–1049, 2001.
Abstract
"A stochastic quantization method for nonlinear problems",
Monte Carlo Methods and Applications, vol. 7(1), pp. 21-34, 2001.
Abstract
Foundations of quantization for probability distributions,
, Secaucus, NJ, USA, Springer-Verlag New York, Inc., 2000.
Abstract
"A space quantization method for numerical integration",
J. Comput. Appl. Math., vol. 89, no. 1, Amsterdam, The Netherlands, Elsevier Science Publishers B. V., pp. 1–38, 1998.
Abstract
"The quantization of the Cantor distribution",
Math. Nachrichten, vol. 183, pp. 113-133, 1997.
Abstract
Vector quantization and signal compression,
: Kluwer Academic Press, 1992.
"Asymptotic quantization error of continuous signals and the quantization dimension",
IEEE Trans. Inform. Theory, vol. IT-28, no. 2, pp. 139–149, March, 1982.
Abstract
"Least squares quantization in PCM",
Information Theory, IEEE Transactions on, vol. 28, no. 2, pp. 129–137, 1982.
Abstract