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Basic properties of the multivariate fractional Brownian motion. (English) Zbl 1293.60044
Chaumont, Loïc (ed.) et al., Self-similar processes and their applications. Selected papers related to the conference, Angers, France, July 20–24, 2009. Paris: Société Mathématique de France (ISBN 978-2-85629-365-2). Séminaires et Congrès 28, 63-84 (2013).
Summary: 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.
For the entire collection see [Zbl 1273.60006].

60G22 Fractional processes, including fractional Brownian motion