This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a pmultivariate self-similar Gaussian process parameterized by p different Hurst exponents Hi, p scaling coefficients σi (of each component) and also by p(p − 1) coefficients ρij, ηij (for i, j = 1, . . . , p with j > i) allowing two components to be more or less strongly correlated and allowing the process to be time reversible or not. We investigate the use of discrete filtering techniques to estimate jointly or separately the different parameters and prove the efficiency of the methodology with a simulation study and the derivation of asymptotic results.

International audienceAnalysis of interactions in the brain in terms of functional resting-state networks has yielded fundamental results in neuroscience. The first step in such analyses of functional connectivity typically involves computing correlations between brain regions. In this paper, we show theoretical results explaining why brain region sizes bias correlation estimators, and propose three new estimators to correct for region size in- fluence. We show experimental results on both synthetic and real fMRI data and discuss the influence of noise and intra-regional correlation on the robustness of the estimators. The bootstrap-based estimator of correlations emerges as the preferred choice