A. Alfonsi, J. Corbetta, J. , and B. , Sampling of one-dimensional probability measures in the convex order and computation of robust option price bounds, International Journal of Theoretical and Applied Finance (IJTAF), vol.22, issue.03, pp.1-41, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01963507

J. Baladron, D. Fasoli, O. Faugeras, and J. Touboul, Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons, J. Math. Neurosci, vol.2, issue.10, p.50, 2012.
URL : https://hal.archives-ouvertes.fr/inserm-00732288

V. Bally and G. Pagès, A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems, Bernoulli, vol.9, issue.6, pp.1003-1049, 2003.

V. Bally, G. Pagès, and J. Printems, A quantization tree method for pricing and hedging multidimensional American options, Math. Finance, vol.15, issue.1, pp.119-168, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00072123

P. Berti, L. Pratelli, and P. Rigo, Gluing lemmas and Skorohod representations, Electron. Commun. Probab, vol.20, issue.53, p.11, 2015.

G. Biau, L. Devroye, and G. Lugosi, On the performance of clustering in Hilbert spaces, IEEE Trans. Inform. Theory, vol.54, issue.2, pp.781-790, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00290855

F. Bolley, Separability and completeness for the Wasserstein distance, Séminaire de probabilités XLI, pp.371-377, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00453887

G. Bormetti, G. Callegaro, G. Livieri, and A. Pallavicini, A backward monte carlo approach to exotic option pricing, European Journal of Applied Mathematics, vol.29, issue.1, pp.146-187, 2018.

M. Bossy and D. Talay, A stochastic particle method for the McKean-Vlasov and the Burgers equation, Math. Comp, vol.66, issue.217, pp.157-192, 1997.

S. Boucheron, G. Lugosi, and P. Massart, A nonasymptotic theory of independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

N. Bouleau, Processus stochastiques et applications. Hermann Paris, 1988.

G. Callegaro, L. Fiorin, and M. Grasselli, Quantized calibration in local volatility, Risk Magazine, vol.28, issue.4, pp.62-67, 2015.

G. Callegaro, L. Fiorin, and M. Grasselli, Pricing via recursive quantization in stochastic volatility models, Quantitative Finance, vol.17, issue.6, pp.855-872, 2017.

J. Chassagneux, L. Szpruch, and A. Tse, Weak quantitative propagation of chaos via differential calculus on the space of measures, 2019.

J. A. Cuesta and C. Matrán, The strong law of large numbers for k-means and best possible nets of Banach valued random variables, Probab. Theory Related Fields, vol.78, issue.4, pp.523-534, 1988.

S. Delattre, S. Graf, H. Luschgy, and G. Pagès, Quantization of probability distributions under norm-based distortion measures ii: Self-similar distributions, Journal of mathematical analysis and applications, vol.318, issue.2, pp.507-516, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00085424

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern classification, 2001.

M. R. El-amri, C. Helbert, O. Lepreux, M. M. Zuniga, C. Prieur et al., Data-driven stochastic inversion via functional quantization, Statistics and Computing, pp.1-17, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02291766

M. El-mikkawy, A note on a three-term recurrence for a tridiagonal matrix, Appl. Math. Comput, vol.139, issue.2-3, pp.503-511, 2003.

A. Fadili, Ordre convexe pour les diffusions multidimensionnelles. Application aux modèles à volatilité locale, 2019.

J. Fort and G. Pagès, On the a.s. convergence of the Kohonen algorithm with a general neighborhood function, Ann. Appl. Probab, vol.5, issue.4, pp.1177-1216, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00709174

N. Fournier and A. Guillin, On the rate of convergence in Wasserstein distance of the empirical measure, Probab. Theory Related Fields, vol.162, issue.3-4, pp.707-738, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00915365

T. Funaki, A certain class of diffusion processes associated with nonlinear parabolic equations, vol.67, pp.331-348, 1984.

J. Gärtner, On the McKean-Vlasov limit for interacting diffusions, Math. Nachr, vol.137, pp.197-248, 1988.

A. Gersho and R. M. Gray, Vector quantization and signal compression, vol.159, 2012.

E. Gobet, G. Pagès, H. Pham, and J. Printems, Discretization and simulation for a class of SPDEs with applications to Zakai and McKean-Vlasov equations, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00003917

E. Gobet, G. Pagès, H. Pham, and J. Printems, Discretization and simulation of the Zakai equation, SIAM J. Numer. Anal, vol.44, issue.6, pp.2505-2538, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00707850

S. Graf and H. Luschgy, Foundations of quantization for probability distributions, Lecture Notes in Mathematics, vol.1730, 2000.

S. Graf, H. Luschgy, and G. Pagès, Optimal quantizers for Radon random vectors in a Banach space, J. Approx. Theory, vol.144, issue.1, pp.27-53, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00211918

L. Grafakos, Classical Fourier analysis, Graduate Texts in Mathematics, vol.249, 2014.

E. Hopf, The partial differential equation u t + uu x = µu xx, Comm. Pure Appl. Math, vol.3, pp.201-230, 1950.

T. Hsing and R. Eubank, Theoretical foundations of functional data analysis, with an introduction to linear operators, 2015.

, IEEE Transactions on Information Theory, issue.2, p.28, 1982.

B. Jourdain, Diffusion processes associated with nonlinear evolution equations for signed measures, Methodol. Comput. Appl. Probab, vol.2, issue.1, pp.69-91, 2000.

B. Jourdain, S. Méléard, and W. A. Woyczynski, Nonlinear SDEs driven by Lévy processes and related PDEs, ALEA Lat. Am. J. Probab. Math. Stat, vol.4, pp.1-29, 2008.

B. Jourdain and G. Pagès, Convex order, quantization and monotone applications of arch models, 2019.

J. L. Kelley, Graduate Texts in Mathematics, 1975.

J. C. Kieffer, Exponential rate of convergence for Lloyd's method. I, IEEE Trans. Inform. Theory, vol.28, issue.2, pp.205-210, 1982.

J. C. Kieffer, Uniqueness of locally optimal quantizer for log-concave density and convex error weighting function, IEEE Trans. Inform. Theory, vol.29, issue.1, pp.42-47, 1983.

V. Koltchinskii, Oracle inequalities in empirical risk minimization and sparse recovery problems, Lecture Notes in Mathematics, vol.2033, 2008.

D. Lacker, Mean field games and interacting particle systems, 2018.

I. B. Lackovi?, On the behaviour of sequences of left and right derivatives of a convergent sequence of convex functions, Publikacije Elektrotehni?kog Fakulteta. Serija Matematika i Fizika, pp.19-27, 1982.

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, p.61, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00393749

T. Linder, Learning-theoretic methods in vector quantization, Principles of nonparametric learning, vol.434, pp.163-210, 2001.

Y. Liu and G. Pagès, Convergence rate of optimal quantization grids and application to empirical measure, 2018.

Y. Liu and G. Pagès, Characterization of probability distribution convergence in wasserstein distance by L p -quantization error function, 2019.

S. P. Lloyd, Least squares quantization in PCM, IEEE Trans. Inform. Theory, vol.28, issue.2, pp.129-137, 1982.

R. Lucchetti, Convexity and well-posed problems, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, vol.22, 2006.

H. Luschgy and G. Pagès, Functional quantization of Gaussian processes, J. Funct. Anal, vol.196, issue.2, pp.486-531, 2002.
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 Lévy processes, Ann. Appl. Probab, vol.18, issue.2, pp.427-469, 2008.

J. Macqueen, Some methods for classification and analysis of multivariate observations, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, vol.I, pp.281-297, 1965.

H. P. Mckean, Propagation of chaos for a class of non-linear parabolic equations, Stochastic Differential Equations (Lecture Series in Differential Equations, pp.41-57, 1967.

G. Pagès, A space quantization method for numerical integration, J. Comput. Appl. Math, vol.89, issue.1, pp.1-38, 1998.

G. Pagès, Quadratic optimal functional quantization of stochastic processes and numerical applications. In Monte Carlo and quasi-Monte Carlo methods, pp.101-142, 2006.

G. Pagès, Introduction to vector quantization and its applications for numerics, CEMRACS 2013-modelling and simulation of complex systems: stochastic and deterministic approaches, vol.48, pp.29-79, 2015.

G. Pagès, Convex order for path-dependent derivatives: a dynamic programming approach, Séminaire de Probabilités XLVIII, pp.33-96, 2016.

G. Pagès, Numerical Probability: An Introduction with Applications to Finance, 2018.

G. Pages, H. Pham, and J. Printems, An optimal markovian quantization algorithm for multi-dimensional stochastic control problems, Stochastics and dynamics, vol.4, issue.04, pp.501-545, 2004.

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

G. Pagès and A. Sagna, Asymptotics of the maximal radius of an L r -optimal sequence of quantizers, Bernoulli, vol.18, issue.1, pp.360-389, 2012.

G. Pagès and A. Sagna, Recursive marginal quantization of the Euler scheme of a diffusion process, Appl. Math. Finance, vol.22, issue.5, pp.463-498, 2015.

G. Pagès and A. Sagna, Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering, Stochastic Process. Appl, vol.128, issue.3, pp.847-883, 2018.

G. Pagès and J. Yu, Pointwise convergence of the Lloyd I algorithm in higher dimension, SIAM J. Control Optim, vol.54, issue.5, pp.2354-2382, 2016.

D. Pollard, Strong consistency of k-means clustering, Ann. Statist, vol.9, issue.1, pp.135-140, 1981.

D. Pollard, A central limit theorem for k-means clustering, Ann. Probab, vol.10, issue.4, pp.919-926, 1982.

D. Pollard, Quantization and the method of k-means, IEEE Trans. Inform. Theory, vol.28, issue.2, pp.199-205, 1982.

G. D. Reis, S. Engelhardt, and G. Smith, Simulation of mckean vlasov sdes with super linear growth, 2018.

W. Rudin, Functional analysis. International Series in Pure and Applied Mathematics, 1991.

A. Sznitman, Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flour XIX-1989, vol.1464, pp.165-251, 1991.

F. Topsoe, Compactness and tightness in a space of measures with the topology of weak convergence, Math. Scand, vol.34, pp.187-210, 1974.

A. V. Trushkin, Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions, IEEE Trans. Inform. Theory, vol.28, issue.2, pp.187-198, 1982.

A. W. Van-der-vaart and J. A. Wellner, Weak convergence and empirical processes, Springer Series in Statistics, 1996.

C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, 2003.

C. Villani, Optimal transport, Old and new, Grundlehren der Mathematischen Wissenschaften, vol.338, 2009.

. Springer-verlag,