A New Rate-Optimal Series Expansion of Fractional Brownian Motion

Mohamed Ndaoud (1)

1 X - École polytechnique

In this paper, we give a new series expansion to simulate B an fBm based on harmonic analysis of the auto-covariance function. We prove that the convergence holds in $L^2$ and uniformly, with a rate-optimal decay of the norm of the rest of the series in both senses. We also give a general framework of rate-optimal series expansion for a class of Gaussian processes. Finally we apply this expansion to functional quantization.

Mots clés: functional quantization; Karhunen - Lòeve; fractional Brownian motion; Fourier series; fractional Orstein - Uhlenbeck

Domaines: Probabilités [math.PR]; Mathématiques [math]

Mohamed Ndaoud. A New Rate-Optimal Series Expansion of Fractional Brownian Motion. 2015. ⟨hal-01273646v2⟩