Mathematics – Probability
Scientific paper
2010-07-06
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.
Amblard Pierre-Olivier
Coeurjolly Jean-François
Lavancier Frédéric
Philippe Anne
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