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

Sylvain Corlay (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Karhunen-Loève basis; Gaussian process; Brownian motion; Brownian bridge; Ornstein-Uhlenbeck; fractional Brownian motion; numerical integration; optimal quantization; product quantization; variance reduction; stratification; integral equation; Nyström method; Gaussian semi-martingale; functional quantization; vector quantization

Domaines: Probabilités [math.PR]

Sylvain Corlay. The Nyström method for functional quantization with an application to the fractional Brownian motion. 2010. ⟨hal-00515488⟩