Ph.d. thesis on vector quantization

Ben Hamida, Optimal quantization: Evolutionary algorithm vs. Pham and J. Printems, Optimal quantization methods and applications to numerical methods and applications in finance, in Handbook of Computational and Numerical Methods in Finance , S.

Rachev Ed. Printems, Optimal quadratic quantization for numerics: the Gaussian case. Monte Carlo Meth.

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Printems, Functional quantization for numerics with an application to option pricing. Printems, www. Website devoted to quantization Vu and R. Gorenflo, Asymptotics of singular values of volterra integral operators. Current usage metrics About article metrics Return to article.

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Round Randomized Learning Vector Quantization for Brain Tumor Imaging

Article Abstract PDF Springer, Berlin Luschgy, The point density measure in the quantization of self-similar probabilities. Cambridge Phil. Gray and D. Neuhoff, Quantization. IEEE Trans.

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Kushner and G. Yin, Stochastic approximation algorithms and applications. First edition, volume 35 of Applications of Mathematics.

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Springer-Verlag, New York , p. Lapeyre, G. Sab, Sequences with low discrepancy. Generalization and application to robbins-monro algorithm. Statistics 21 — Luschgy and G.

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Mrad and S. The explosion of computing capabilities in recent decades has both been a motivation and a driving force behind the development of such numerical methods. Meanwhile, a new field emerged last decade under the name "functional quantization". This is to extend the concept to the infinite dimensional setting.

From applications viewpoint, it comes to optimally discretize the path space of a stochastic process that is to say, a dynamic random phenomenon. The archetype of such a process is the Brownian motion.

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These recent works are the basis of path-dependent option pricing methods discussed below. See [4]. The first chapter of Afef Sellami's PhD thesis [2] is an excellent introduction to optimal quantization in French.

The introduction is available separately. In [5] , principal quantization-based numerical methods for finance are reviewed.