Basic properties of the Multivariate Fractional Brownian Motion

Details Basic properties of the Multivariate Fractional Brownian Motion Basic properties of the Multivariate Fractional Brownian Motion

2010-07-06

arxiv.org/abs/1007.0828v2

Mathematics

Probability

D\'epartement Images et Signal

Scientific paper

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.

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