Apparaît dans la collection : Les probabilités de demain 2017

In this talk, we give a new series expansion to simulate B a fractional Brownian motion based on harmonic analysis of the auto-covariance function. The construction proposed here reveals a link between Karhunen-Loève theorem and harmonic analysis for Gaussian processes with stationarity conditions. We also show some results on the convergence. In our case, the convergence holds in L2 and uniformly, with a rate-optimal decay of the norm of the rest of the series in both senses.