The Nyström method for functional quantization with an application to the fractional Brownian motion
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.
Keywords
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
Domains
Probability [math.PR]
Origin : Files produced by the author(s)
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