Free Access
Issue
ESAIM: PS
Volume 12, April 2008
Page(s) 127 - 153
DOI https://doi.org/10.1051/ps:2007044
Published online 23 January 2008
  1. V. Bally and C. Pagès, A quantization algorithm for solving discrete time multidimensional optimal stopping problems. Bernoulli 9 (2003) 1003–1049. [CrossRef] [MathSciNet]
  2. V. Bally, C. Pagès and J. Printems, First order schemes in the numerical quantization method. Mathematical Finance 13 (2001) 1–16. [CrossRef]
  3. J.A. Bucklew and G.L. Wise, Multidimensional asymptiotic quantization theory with r-th power distortion measure. IEEE Trans. Inform. Theory, 28, Special issue on quantization, A. Gersho & R.M. Grey Eds., (1982) 239–247.
  4. S. Delattre, S. Graf, H. Luschgy and G. Pagès, Quantization of probability distributions under norm-based distortion measures. Statist. Decisions 22 (2004) 261–282. [CrossRef] [MathSciNet]
  5. S. Delattre, J.C. Fort and G. Pagès, Local distortion and µ-mass of the cells of one dimensional asymptotically optimal quantizers. Comm. Statist. Theory Methods 33 (2004) 1087–1117. [CrossRef] [MathSciNet]
  6. S. Graf and H. Luschgy, Foundations of Quantization for Probability Distributions. Lect. Notes in Math. 1730, Springer, Berlin (2000).
  7. S. Graf and H. Luschgy, Rates of convergence for the empirical quantization error. Ann. Probab. 30 (2002) 874–897. [CrossRef] [MathSciNet]
  8. H. Luschgy and G. Pagès, Functional quantization of stochastic processes. J. Funct. Anal. 196 (2002) 486–531. [CrossRef] [MathSciNet]
  9. H. Luschgy and G. Pagès, Sharp asymptotics of the functional quantization problem for Gaussian processes. Ann. Probab. 32 (2004) 1574–1599. [CrossRef] [MathSciNet]
  10. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press (1995).
  11. G. Pagès, A space vector quantization method for numerical integration. J. Comput. Appl. Math. 89 (1997) 1–38.
  12. G. Pagès and J. Printems, Functional quantization for numerics with an application to option pricing. Monte Carlo Methods & Applications 11 (2005) 407–446. [CrossRef]
  13. A. Sellami, Quantization based filtering method using first order approximation. Pré-pub. LPMA-1009 (2005). To appear in SIAM J. Numerical Analysis.
  14. P.L. Zador, Development and evaluation of procedures for quantizing multivariate distributions. Ph.D. thesis, Stanford University (1963).
  15. P.L. Zador, Asymptotic quantization error of continuous signals and the quantization dimension. IEEE Trans. Inform. Theory 28, Special issue on quantization, A. Gersho & R.M. Grey Eds. (1982) 139–149.

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