HAL: hal-00497639, version 2

arXiv: 1007.0828

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v2 (2012-04-25)

Basic properties of the Multivariate Fractional Brownian Motion

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

(2010-07-05)

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.

1:	Grenoble Images Parole Signal Automatique (GIPSA-lab)
	CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
2:	Laboratoire Jean Kuntzmann (LJK)
	CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
3:	Laboratoire de Mathématiques Jean Leray (LMJL)
	CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Self similarity – Multivariate process – Long-range dependence – Superlinear process – Increment process – Limit theorem

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From: Anne Philippe <>

Submitted on: Wednesday, 25 April 2012 16:08:20

Updated on: Wednesday, 25 April 2012 16:28:12