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

Abstract: In this article, the so-called "Nystr\"om 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-Lo`eve decomposition. A numerical test of the "functional stratification" variance reduction algorithm is performed with the fractional Brownian motion.