Y. Achdou and O. Pironneau, Computational Methods for Option Pricing, SIAM series, Frontiers in Applied Mathematics, p.297, 2005.

V. Bally and G. Pagès, A quantization algorithm for solving multidimensional discrete-time optimal stopping problems, Bernoulli, vol.9, issue.6, pp.1003-1049, 2003.
DOI : 10.3150/bj/1072215199
URL : https://hal.archives-ouvertes.fr/hal-00104798

V. Bally and G. Pagès, Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Processes and their Applications, vol.106, issue.1, pp.1-40, 2003.
DOI : 10.1016/S0304-4149(03)00026-7
URL : https://hal.archives-ouvertes.fr/hal-00103987

V. Bally, G. Pagès, and J. Printems, A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS, Mathematical Finance, vol.26, issue.2, pp.119-168, 2005.
DOI : 10.1287/moor.27.1.121.341
URL : https://hal.archives-ouvertes.fr/hal-00101786

A. Bensoussan, On the theory of option pricing, Acta Appl. Math, vol.2, pp.139-158, 1984.

A. Bensoussan and J. Lions, Applications des inéquations variationnelles en contrôle stochastique, p.525, 1978.

V. Bally and D. Talay, The distribution of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function, Probab. Theory Related Fields, pp.43-60, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074427

A. Benveniste, M. Métivier, and P. Priouret, Algorithmes adaptatifs and approximations stochastiques Adaptive Algorithms and Stochastic Approximations, p.380, 1987.

A. Beskos and G. O. Roberts, Exact simulation of diffusions, The Annals of Applied Probability, vol.15, issue.4, pp.2422-2444, 2005.
DOI : 10.1214/105051605000000485

G. Biau, L. Devroye, and G. Lugosi, On the Performance of Clustering in Hilbert Spaces, IEEE Transactions on Information Theory, vol.54, issue.2, pp.781-790, 2008.
DOI : 10.1109/TIT.2007.913516
URL : https://hal.archives-ouvertes.fr/hal-00290855

N. Bouleau and D. Lépingle, Numerical methods for stochastic processes, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, p.359, 1994.

A. Brancolini, G. Butazzo, F. Santambrogio, and E. Stepanov, short-term planning in the asymptotical location problem, ESAIM: Control, Optimisation and Calculus of Variations, vol.15, issue.3, pp.509-524, 2009.
DOI : 10.1051/cocv:2008034

A. Brandejsky, B. De-saporta, and F. Dufour, Optimal stopping for partially observed piecewise-deterministic Markov processes, Stochastic Processes and their Applications, pp.3201-3238, 2013.
DOI : 10.1016/j.spa.2013.03.006
URL : https://hal.archives-ouvertes.fr/hal-00755119

A. Brandejsky, B. De-saporta, and F. Dufour, Numerical method for impulse control of piecewise deterministic Markov processes, Automatica, issue.5, pp.48-779, 2012.

J. A. Bucklew and G. L. Wise, Multidimensional Asymptotic Quantization Theory with r th Power Distortion Measures, IEEE Transactions on Information Theory, issue.2, pp.28-239, 1988.

H. Cardot, P. Cénac, and J. Monnez, A fast and recursive algorithm for clustering large datasets with -medians, Computational Statistics & Data Analysis, vol.56, issue.6, pp.1431-1449, 2012.
DOI : 10.1016/j.csda.2011.11.019
URL : https://hal.archives-ouvertes.fr/hal-00644683

S. Corlay, Some aspects of optimal quantization and applications to finance, Thèse de l'UPMC, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00626445

S. Corlay and G. Pagès, Functional quantization based stratified sampling methods, to appear in Monte Carlo Methods and Appl, 2014.

M. Corsi, H. Pham, and W. Runggaldier, Numerical approximation by quantization of control problems in finance under partial observation, chapter from Mathematical Modeling and Numerical Methods in Finance (special volume, Handbook of Numerical Analysis 15, pp.325-360, 2008.

T. Cover and J. Thomas, Elements of Information Theory, p.748, 2006.

J. A. Cuesta-albertos and C. Matrán, The strong law of large numbers for k-means and best possible nets of Banach valued random variables, pp.523-534, 1988.

S. Delattre, S. Graf, H. Luschgy, and G. Pagès, Quantization of probability distributions under norm-based distortion measures, Statistics & Decisions, vol.22, issue.4/2004, pp.261-282, 2004.
DOI : 10.1524/stnd.22.4.261.64314
URL : https://hal.archives-ouvertes.fr/hal-00003057

A. Dembo and O. Zeitouni, Large deviations techniques and applications. Corrected reprint of the second, Stochastic Modeling and Applied Probability, p.396, 1998.

S. Dereich, The coding complexity of diffusion processes under L p ([0, 1])-norm distortion, Stochastic Process, Appl, vol.118, issue.6, pp.938-951, 2007.

Q. Du, V. Faber, and M. Gunzburger, Centroidal Voronoi Tessellations: Applications and Algorithms, SIAM Review, vol.41, issue.4, pp.637-676, 1999.
DOI : 10.1137/S0036144599352836

Q. Du, M. Emelianenko, and L. Ju, Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations, SIAM Journal on Numerical Analysis, vol.44, issue.1, pp.102-119, 2006.
DOI : 10.1137/040617364

M. Duflo, Algorithmes stochastiques, coll, Mathématiques & Applications, vol.23, p.319, 1997.

. Fourniéfournié´fourniéé, J. M. Lasry, J. Lebuchoux, P. Lions, and N. Touzi, Some applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics, vol.3, pp.391-412, 1999.

J. H. Friedman, J. L. Bentley, and R. A. Finkel, An Algorithm for Finding Best Matches in Logarithmic Expected Time, ACM Transactions on Mathematical Software, vol.3, issue.3, pp.209-226, 1977.
DOI : 10.1145/355744.355745

A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, Springer International Series in Engineering and Computer Science, vol.159, p.732, 1991.
DOI : 10.1007/978-1-4615-3626-0

P. Glasserman, Monte Carlo Methods in Financial Engineering, p.596, 2003.
DOI : 10.1007/978-0-387-21617-1

E. Gobet, G. Pagès, H. Pham, and J. Printems, Discretization and Simulation of the Zakai Equation, SIAM Journal on Numerical Analysis, vol.44, issue.6, pp.2505-2538, 2007.
DOI : 10.1137/050623140
URL : https://hal.archives-ouvertes.fr/hal-00394974

S. Graf and H. Luschgy, Foundations of Quantization for Probability Distributions. LNM 1730, 2000.

S. Graf and H. Luschgy, Rates of convergence for the empirical quantization error, The Annals of Probability, vol.30, issue.2, pp.874-897, 2002.
DOI : 10.1214/aop/1023481010

S. Graf, H. Luschgy, and G. Pagès, Optimal quantizers for Radon random vectors in a Banach space, Journal of Approximation Theory, vol.144, issue.1, pp.27-53, 2007.
DOI : 10.1016/j.jat.2006.04.006
URL : https://hal.archives-ouvertes.fr/hal-00004668

S. Graf, H. Luschgy, and G. Pagès, Distortion mismatch in the quantization of probability measures, ESAIM: Probability and Statistics, vol.12, pp.127-154, 2008.
DOI : 10.1051/ps:2007044
URL : https://hal.archives-ouvertes.fr/hal-00019228

S. Graf, H. Luschgy, and G. Pagès, The local quantization behavior of absolutely continuous probabilities, The Annals of Probability, vol.40, issue.4, pp.1795-1828, 2012.
DOI : 10.1214/11-AOP663
URL : https://hal.archives-ouvertes.fr/hal-00730490

D. A. Huffman, A method for the construction of minimum-redundancy codes, Proc. IRE, pp.1098-1101, 1952.
DOI : 10.1007/BF02837279

P. Jaillet, D. Lamberton, and B. Lapeyre, Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990.
DOI : 10.1007/BF00047211

J. C. Kieffer, Exponential rate of convergence for Lloyd's method I, IEEE Transactions on Information Theory, vol.28, issue.2, pp.28205-210, 1982.
DOI : 10.1109/TIT.1982.1056482

H. J. Kushner and G. G. Yin, Stochastic approximation and recursive algorithms and applications, p.474, 2003.

D. Lamberton and B. Lapeyre, Introduction to stochastic calculus applied to finance, p.185, 1996.

B. Lapeyre, . Pardouxépardoux´pardouxé, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, coll. Oxford Texts in Applied and Engineering Mathematics, p.176, 2003.

D. Lamberton, Optimal stopping and American options, Ljubljana Summer School on Financial Mathematics, 2009.

A. Lejay and V. Reutenauer, A variance reduction technique using a quantized Brownian motion as a control variate, The Journal of Computational Finance, vol.16, issue.2, pp.61-84, 2012.
DOI : 10.21314/JCF.2012.242
URL : https://hal.archives-ouvertes.fr/inria-00393749

F. A. Longstaff and E. S. Schwarz, Valuing American Options by Simulation: A Simple Least-Squares Approach, Review of Financial Studies, vol.14, issue.1, pp.113-148, 2001.
DOI : 10.1093/rfs/14.1.113

H. Luschgy and G. Pagès, Functional quantization of Gaussian processes, Journal of Functional Analysis, vol.196, issue.2, pp.486-531, 2002.
DOI : 10.1016/S0022-1236(02)00010-1
URL : https://hal.archives-ouvertes.fr/hal-00102159

H. Luschgy and G. Pagès, Sharp asymptotics of the functional quantization problem for Gaussian processes, Ann. Probab, vol.32, pp.1574-1599, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00102159

H. Luschgy and G. Pagès, Functional quantization rate and mean regularity of processes with an application to L??vy processes, The Annals of Applied Probability, vol.18, issue.2, pp.427-469, 2008.
DOI : 10.1214/07-AAP459

H. Luschgy and G. Pagès, Greedy vector quantization, pré-pub. LPMA 1624, submitted for publication, 2014.
DOI : 10.1016/j.jat.2015.05.005
URL : http://arxiv.org/abs/1409.0732

J. Mcnames, A fast nearest-neighbor algorithm based on a principal axis search tree, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.9, pp.964-976, 2001.
DOI : 10.1109/34.955110

J. M. Mirebeau and A. Cohen, Greedy bisection generates optimally adapted triangulations, Mathematics of Computation, vol.81, issue.278, pp.811-837, 2012.
DOI : 10.1090/S0025-5718-2011-02459-2
URL : https://hal.archives-ouvertes.fr/hal-00387416

J. Neveu, MartingalesàMartingalesà temps discret English translation: Discrete-parameter martingales, pp.218-236, 1972.

H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF regional conference series in Applied mathematics, p.241, 1992.

G. Pagès, A space quantization method for numerical integration, Proceedings of the ESANN' 93, M. Verleysen Bruxelles, Quorum Editions, pp.1-38, 1993.
DOI : 10.1016/S0377-0427(97)00190-8

G. Pagès, Introduction to Numerical Probability and Applications to Finance, to appear, coll. Universitext, Springer. Preliminary version available at www, 2014.

G. Pagès and H. Pham, Optimal quantization methods for nonlinear filtering with discrete-time observations, Bernoulli, vol.11, issue.5, pp.893-932, 2005.
DOI : 10.3150/bj/1130077599

G. Pagès, H. Pham, and J. Printems, AN OPTIMAL MARKOVIAN QUANTIZATION ALGORITHM FOR MULTI-DIMENSIONAL STOCHASTIC CONTROL PROBLEMS, Stochastics and Dynamics, vol.04, issue.04, pp.501-545, 2004.
DOI : 10.1142/S0219493704001231

G. Pagès and J. Printems, Optimal quadratic quantization for numerics: the Gaussian case, Monte Carlo Methods and Applications, vol.9, issue.2, pp.135-165, 2003.
DOI : 10.1515/156939603322663321

G. Pagès and J. Printems, Functional quantization for numerics with an application to option pricing, Monte Carlo Methods and Applications, vol.11, issue.4, pp.407-446, 2005.
DOI : 10.1515/156939605777438578

G. Pagès and J. Printems, Optimal quantization for finance: from random vectors to stochastic processes, chapter from Mathematical Modeling and Numerical Methods in Finance (special volume, coll. Handbook of Numerical Analysis, pp.595-649, 2009.

G. Pagès, H. Pham, and J. Printems, Optimal quantization methods and applications to numerical problems in finance, Handbook on Numerical Methods in Finance, Birkhauser, pp.253-298, 2005.

G. Pagès and B. Wilbertz, Dual quantization for random walks with application to credit derivatives, The Journal of Computational Finance, vol.16, issue.2, pp.33-60, 2012.
DOI : 10.21314/JCF.2012.239

G. Pagès and B. Wilbertz, Intrinsic Stationarity for Vector Quantization: Foundation of Dual Quantization, SIAM Journal on Numerical Analysis, vol.50, issue.2, pp.747-780, 2012.
DOI : 10.1137/110827041

G. Pagès and B. Wilbertz, Optimal Delaunay et Voronoi quantization methods for pricing American options, Numerical methods in Finance, pp.171-217, 2012.

G. Pagès and Y. J. Xiao, Sequences with low discrepancy and pseudo-random numbers:theoretical results and numerical tests, Journal of Statistical Computation and Simulation, vol.185, issue.2, pp.163-183, 1997.
DOI : 10.1016/0022-314X(91)90055-G

G. Pagès and J. Yu, Pointwise convergence of the Lloyd algorithm in higher dimension, pré-pub PMA 1604, 2013.

H. Pham, W. Runggaldier, and A. Sellami, Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation, Monte Carlo Methods and Applications, vol.11, issue.1, pp.57-81, 2004.
DOI : 10.1515/1569396054027283
URL : https://hal.archives-ouvertes.fr/hal-00002973

D. Pollard, A Central Limit Theorem for $k$-Means Clustering, The Annals of Probability, vol.10, issue.4, pp.919-926, 1982.
DOI : 10.1214/aop/1176993713

P. D. Proinov, Discrepancy and integration of continuous functions, Journal of Approximation Theory, vol.52, issue.2, pp.121-131, 1988.
DOI : 10.1016/0021-9045(88)90051-2

C. E. Shannon, A mathematical theory of communication, bell Syst Discrepancy and integration of continuous functions, Tech. J. J. of Approx. Theory, vol.27, issue.52, pp.376-423, 1948.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, p.144, 1949.

A. N. Shiryaev, Optimal Stopping Rules, Applications of Mathematics, p.232, 2007.
DOI : 10.1007/978-3-642-04898-2_433

D. Talay and L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Analysis and Applications, vol.20, issue.4, pp.94-120, 1990.
DOI : 10.1080/07362999008809220
URL : https://hal.archives-ouvertes.fr/inria-00075490

T. Tarpey, L. Li, and B. Flury, Principal Points and Self-Consistent Points of Elliptical Distributions, The Annals of Statistics, vol.23, issue.1, pp.103-112, 1995.
DOI : 10.1214/aos/1176324457

S. Villeneuve and A. Zanette, Parabolic ADI Methods for Pricing American Options on Two Stocks, Mathematics of Operations Research, vol.27, issue.1, pp.121-149, 2002.
DOI : 10.1287/moor.27.1.121.341

P. L. Zador, Asymptotic quantization error of continuous signals and the quantization dimension, IEEE Transactions on Information Theory, vol.28, issue.2, pp.28139-28153, 1982.
DOI : 10.1109/TIT.1982.1056490