Basic properties of the Multivariate Fractional Brownian Motion

Pierre-Olivier Amblard (1) , Jean-François Coeurjolly (1, 2) , Frédéric Lavancier (3) , Anne Philippe (3)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 FIGAL - Fiabilité et Géométrie Aléatoire
3 LMJL - Laboratoire de Mathématiques Jean Leray

This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm's may be reached as the limit of partial sums of (super)linear processes. Finally, an algorithm to perfectly simulate the mfBm is presented and illustrated by some simulations.

Mots clés: Limit theorem; Increment process; Self similarity; Multivariate process; Long-range dependence; Superlinear process

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre-Olivier Amblard, Jean-François Coeurjolly, Frédéric Lavancier, Anne Philippe. Basic properties of the Multivariate Fractional Brownian Motion. Séminaires et congrès, 2013, 28, pp.65-87. ⟨hal-00497639v2⟩