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Publications
Vector quantization and signal compression,
: Kluwer Academic Press, 1992.
"Universal $L^s$-rate-optimality of $L^r$-optimal quantizers by dilatation and contraction",
ESAIM: Probability and Statistics, vol. 13, pp. 218-246, 2009.
Abstract
"A stochastic quantization method for nonlinear problems",
Monte Carlo Methods and Applications, vol. 7(1), pp. 21-34, 2001.
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
"Small ball probabilities around random centers of Gaussian measures and applications to quantization",
J. Theor. Probab., vol. 16(2), pp. 427-449, 2003.
Abstract
"Sharp asymptotics of the Kolmogorov entropy for Gaussian measures",
Journal of Functional Analysis, vol. 212, no. 1, pp. 89 - 120, 2004.
Abstract
Sharp asymptotics of the functional quantization problem for Gaussian processes,
, vol. 32, no. 2, 2004.
Abstract
"Rates of convergence for the empirical quantization error",
Ann. Probab., vol. 30, pp. 874- 897, 2002.
"A quantization tree method for pricing and hedging multidimensional American options",
Mathematical Finance, vol. 15, no. 1, pp. 119-168, 2005.
Abstract
Download: Quantization-Tree.pdf (483.24 KB)
"The quantization of the Cantor distribution",
Math. Nachrichten, vol. 183, pp. 113-133, 1997.
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
"Quantization for probability measures with respect to the geometric mean error",
Math. Proc. Cambridge Phil. Soc., vol. 136, pp. 687-717, 2004.
"Quantization for probability measures in the Prokhorov metric",
Theory Probab. Appl., vol. 53, pp. 216-241, 2009.
Abstract
"The quantization dimension of self-similar probabilities",
Math. Nachrichten, vol. 241, pp. 103-109 , 2002.
"Quantization based filtering method using first order approximation",
SIAM journal on numerical analysis, vol. 47, issue 6, pp. 4711-4734 , 2010.
Abstract
"A quantization algorithm for solving multidimensional optimal stopping problems, preprint",
University de Paris VI, pp. 1003–1049, 2001.
Abstract
"Pricing path-dependent options using optimized functional quantization",
Numerical Methods in Finance, 2006.
Download: Pricing Path Dependent Option Using Functional Quantization.pdf (762.71 KB)
"The point density measure in the quantization of self-similar probabilities",
Math. Proc. Cambridge Phil. Soc. , vol. 138, pp. 513-531, 2005.
Partial functional quantization and generalized bridges,
, 2011.
Abstract
Download: partial quantization.pdf (392.92 KB)
"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