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Publications
"Optimal quantization methods for nonlinear filtering with discrete-time observations",
Bernoulli, vol. 11(5), 2005.
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
Partial functional quantization and generalized bridges,
, 2011.
Abstract
Download: partial quantization.pdf (392.92 KB)
"The point density measure in the quantization of self-similar probabilities",
Math. Proc. Cambridge Phil. Soc. , vol. 138, pp. 513-531, 2005.
"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)
"A quantization algorithm for solving multidimensional optimal stopping problems, preprint",
University de Paris VI, pp. 1003–1049, 2001.
Abstract
"Quantization based filtering method using first order approximation",
SIAM journal on numerical analysis, vol. 47, issue 6, pp. 4711-4734 , 2010.
Abstract
"The quantization dimension of self-similar probabilities",
Math. Nachrichten, vol. 241, pp. 103-109 , 2002.
"Quantization for probability measures in the Prokhorov metric",
Theory Probab. Appl., vol. 53, pp. 216-241, 2009.
Abstract
"Quantization for probability measures with respect to the geometric mean error",
Math. Proc. Cambridge Phil. Soc., vol. 136, pp. 687-717, 2004.
"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
"The quantization of the Cantor distribution",
Math. Nachrichten, vol. 183, pp. 113-133, 1997.
Abstract
"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)
"Rates of convergence for the empirical quantization error",
Ann. Probab., vol. 30, pp. 874- 897, 2002.
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
"Small ball probabilities around random centers of Gaussian measures and applications to quantization",
J. Theor. Probab., vol. 16(2), pp. 427-449, 2003.
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
"A stochastic quantization method for nonlinear problems",
Monte Carlo Methods and Applications, vol. 7(1), pp. 21-34, 2001.
Abstract
"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