The Nyström method for functional quantization with an application to the fractional Brownian motion

TitleThe Nyström method for functional quantization with an application to the fractional Brownian motion
Publication TypeJournal Article
Year of Publication2010
AuthorsSylvain Corlay
KeywordsBrownian bridge, Brownian motion, fractional Brownian motion, functional quantization, Gaussian process, Gaussian semi-martingale, integral equation, Karhunen-Loève basis, numerical integration, Nyström method, optimal quantization, Ornstein-Uhlenbeck, product quantization, stratification, Variance reduction, vector quantization
Abstract

In this article, the so-called "Nyström method" is tested to compute optimal quantizers of Gaussian processes. In particular, we derive the optimal quantization of the fractional Brownian motion by approximating the first terms of its Karhunen-Loève decomposition.
A numerical test of the "functional stratification" variance reduction algorithm is performed with the fractional Brownian motion.

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