Publications

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2014
2013
2012
Gilles Pagès, and Benedikt Wilbertz, "Dual Quantization for random walks with application to credit derivatives", Journal of Computational Finance, vol. 16, issue 2, pp. 33--60, 2012. Abstract
Sylvain Corlay, Joachim Lebovits, and Jacques Lévy Véhel, "Multifractional stochastic volatility models", Mathematical Finance, vol. 24, issue 2, pp. 364-402, 2012. Abstract  Download: Multifractional Stochastic Volatility.pdf (759.01 KB)
Romain Azaïs, Anne Gégout-Petit, and Jérôme Saracco, "Optimal quantization applied to sliced inverse regression", Journal of Statistical Planning and Inference, vol. 142, issue 2, pp. 481–492, 2012. Abstract
Abass Sagna, "Pricing of barrier options by marginal functional quantization", Monte Carlo Methods and Applications, vol. 17, issue 4, pp. 371--398, 2012. Abstract  Download: Pricing barrier options by marginal functional quantization.pdf (168.74 KB)
2011
Steffen Dereich, Michael Scheutzow, and Reik Schottstedt, "Constructive quantization: approximation by empirical measures", Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 2011. Abstract
Benoît Patra, "Convergence of distributed asynchronous learning vector quantization algorithms", Journal of Machine Learning Research, pp. 3431-3466, 2011. Abstract  Download: AsyncStochGradient.pdf (498.47 KB)
Steffen Dereich, and Christian Vormoor, "The high resolution vector quantization problem with Orlicz norm distortion", Journal ot Theoretical Probability, vol. 24, issue 2, pp. 517-544, 2011. Abstract
Noufel Frikha, and Abass Sagna, "Quantization-based recursive importance sampling", Monte Carlo Methods and Applications, vol. 18, issue 4, pp. 287--326, 2011. Abstract  Download: Frikha Sagna - Quantization based Recursive Importance Sampling.pdf (521.63 KB)
2010
Harald Luschgy, Siegfried Graf, and Gilles Pagès, "Fractal functional quantization of mean-regular stochastic processes", Mathematical Proceedings of the Cambridge Philosophical Society, 2010. Abstract
Afef Sellami, "Quantization-based filtering method using first order approximation", SIAM journal on numerical analysis, vol. 47, issue 6, pp. 4711-4734, 2010. Abstract
Olivier Bardou, Sandrine Bouthemy, and Gilles Pagès, "When are Swing options bang-bang and how to use it", International Journal of Theoretical and Applied Finance, vol. 13, issue 6, pp. 867-899, 2010. Abstract
2009
Steffen Dereich, "Asymptotic formulae for coding problems and intermediate optimization problems: a review", Trends in Stochastic Analysis: Cambridge University Press, pp. 187-232, 2009. Abstract
Frank Aurzada, and Steffen Dereich, "The coding complexity of Lévy processes", Foundations of Computational Mathematics, vol. 9, issue 3, pp. 359-390, 2009. Abstract
Olivier Bardou, Sandrine Bouthemy, and Gilles Pagès, "Optimal quantization for the pricing of swing options", Applied Mathematical Finance, vol. 16, issue 2, pp. 183-217, 2009. Abstract
Harald Luschgy, and Siegfried Graf, "Quantization for probability measures in the Prokhorov metric", Theory of Probability and Its Applications, vol. 53, pp. 216-241, 2009. Abstract
2008
Steffen Dereich, "The coding complexity of diffusion processes under Lp([0, 1])-norm distortion", Stochastic Processes and their Applications, vol. 118, issue 6, pp. 938-951, June, 2008. Abstract
Steffen Dereich, "The coding complexity of diffusion processes under supremum norm distortion", Stochastic Processes and their Applications, vol. 118, issue 6, pp. 917-937, 2008. Abstract
Afef Sellami, "Comparative survey on nonlinear filtering methods: the quantization and the particle filtering approaches", Journal of Statistical Computation and Simulation, vol. 78, issue 2, pp. 93-113, 2008. Abstract
Gilles Pagès, "Quadratic optimal functional quantization of stochastic processes and numerical applications", Monte Carlo and Quasi-Monte Carlo Methods 2006: Springer Berlin Heidelberg, pp. 101-142, 2008. Abstract
2007
Siegfried Graf, Harald Luschgy, and Gilles Pagès, "Optimal quantizers for Radon random vectors in a Banach space", Journal of Approximation Theory, vol. 144, no. 1, Orlando, FL, USA, Academic Press, Inc., pp. 27–53, 2007. Abstract
2006
Emmanuel Gobet, Gilles Pagès, Huyên Pham, and Jacques Printems, "Discretization and Simulation of the Zakai Equation", SIAM Journal on Numerical Analysis, vol. 44, issue 6, pp. 2505-2538, 2006. Abstract
François Delarue, and Stéphane Menozzi, "A forward–backward stochastic algorithm for quasi-linear PDEs", Annals of Applied Probability, vol. 16, issue 1, pp. 140-184, 2006. Abstract
Harald Luschgy, and Gilles Pagès, "Functional quantization of a class of Brownian diffusions: a constructive approach", Stochastic Processes and their Applications, vol. 116, no. 2, pp. 310-336, 2006. Abstract
Moez Mrad, and Sana Ben Hamida, "Optimal quantization : evolutionary algorithm vs stochastic gradient", Proceedings of the 9th Joint Conference on Information Sciences: Atlantic Press, 2006. Abstract  Download: Evolutionary-Algorithms.pdf (195.2 KB)
2005
Gilles Pagès, and Jacques Printems, "Functional quantization for numerics with an application to option pricing", Monte Carlo Methods and Appl., vol. 11, no. 11, pp. 407-446, 2005. Abstract  Download: Functional Quantization Num.pdf (531.76 KB)
Harald Luschgy, and Siegfried Graf, "The point density measure in the quantization of self-similar probabilities", Mathematical Proceedings of the Cambridge Philosophical Society, vol. 138, pp. 513-531, 2005.
2004
Gilles Pagès, Huyên Pham, and Jacques Printems, "Optimal quantization methods and applications to numerical problems in finance", Handbook on Numerical Methods in Finance: Birkhäuser, Boston, MA, pp. 253-298, 2004. Abstract
Harald Luschgy, and Siegfried Graf, "Quantization for probability measures with respect to the geometric mean error", Mathematical Proceedings of the Cambridge Philosophical Society, vol. 136, pp. 687-717, 2004.
Harald Luschgy, and Gilles Pagès, "Sharp asymptotics of the functional quantization problem for Gaussian processes", Annals of Probability, vol. 32, issue 2, no. 2, pp. 1574-1599, 2004. Abstract
Harald Luschgy, and Gilles Pagès, "Sharp asymptotics of the Kolmogorov entropy for Gaussian measures", Journal of Functional Analysis, vol. 212, no. 1, pp. 89-120, 2004. Abstract
2003
Thaddeus Tarpey, and Kimberly T. J. Kinateder, "Clustering functional data", Journal of Classification, vol. 20, pp. 93-114, 2003. Abstract
Vlad Bally, and Gilles Pagès, "Error analysis of the quantization algorithm for obstacle problems", Stochastic Processes & Their Applications, vol. 106, issue 1, pp. 1-40, 2003. Abstract
Vlad Bally, Gilles Pagès, and Jacques Printems, "First order schemes in the numerical quantization method", Mathematical Finance, vol. 13, issue 1, pp. 1-16, 2003. Abstract  Download: First Order Schmes.pdf (218.51 KB)
Siegfried Graf, Harald Luschgy, and Gilles Pagès, "Functional quantization and small balls probabilities for Gaussian processes", Journal of Theoretical Probability, vol. 16, issue 4, pp. 1047-1062, 2003. Abstract
Gilles Pagès, and Jacques Printems, "Optimal quadratic quantization for numerics: the Gaussian case", Monte Carlo Methods and Applications, vol. 9, pp. 135–166, 2003. Abstract  Download: Gaussian Case.pdf (563.34 KB)
2002
Harald Luschgy, and Gilles Pagès, "Functional quantization of Gaussian processes", Journal of Functional Analysis, vol. 196, no. 2: Academic Press, pp. 486–531, December, 2002. Abstract
Jean-Claude Fort, and Gilles Pagès, "Asymptotics of optimal quantizers for some scalar distributions", Journal of Computational and Applied Mathematics, vol. 146, no. 2, Amsterdam, The Netherlands, The Netherlands, Elsevier Science Publishers B. V., pp. 253–275, 2002. Abstract
Harald Luschgy, and Siegfried Graf, "The quantization dimension of self-similar probabilities", Mathematische Nachrichten, vol. 241, pp. 103-109, 2002.
Harald Luschgy, and Siegfried Graf, "Rates of convergence for the empirical quantization error", Annals of Probability, vol. 30, pp. 874-897, 2002.
2001
Harald Luschgy, and Siegfried Graf, "Asymptotics of the quantization errors for self-similar probabilities", Real Analysis Exchange 26, vol. 26, issue 2, pp. 795-810, 2001.
Vlad Bally, Gilles Pagès, and Jacques Printems, "A stochastic quantization method for nonlinear problems", Monte Carlo Methods and Applications, vol. 7, issue 1, pp. 21-34, 2001. Abstract
2000
Siegfried Graf, and Harald Luschgy, "Foundations of quantization for probability distributions", Lecture notes in mathematics, Secaucus, NJ, USA, Springer-Verlag New York, Inc., 2000. Abstract
1998
Gilles Pagès, "A space quantization method for numerical integration", Journal of Computational and Applied Mathematics, vol. 89, no. 1, Amsterdam, The Netherlands, Elsevier Science Publishers B. V., pp. 1–38, 1998. Abstract
1997
Harald Luschgy, and Siegfried Graf, "The quantization of the Cantor distribution", Mathematische Nachrichten, vol. 183, pp. 113-133, 1997. Abstract
1995
1992
Allen Gersho, and Robert M. Gray, "Vector quantization and signal compression", Kluwer international series in engineering and computer science: Kluwer Academic Press, 1992.
1982
Paul L. Zador, "Asymptotic quantization error of continuous signals and the quantization dimension", IEEE Transactions on Information Theory, vol. 28, issue 2, pp. 139–149, March, 1982. Abstract
Stuart P. Lloyd, "Least squares quantization in PCM", IEEE Transactions on Information Theory, vol. 28, issue 2, pp. 129–137, 1982. Abstract
James A. Bucklew, and Gary L. Wise, "Multidimensional asymptotic quantization theory with rth power distortion measures", IEEE Transactions on Information Theory, vol. 28, issue 2, pp. 239-247, 1982. Abstract