BASIC PROPERTIES OF THE MULTIVARIATE FRACTIONAL BROWNIAN MOTION by
نویسندگان
چکیده
— 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. Résumé (Propriétés du mouvement brownien fractionnaire multivarié) Cet article constitue une synthèse des propriétés du mouvement brownien fractionnaire multivarié (mBfm) et de ses accroissements. Différentes caractérisations du mBfm sont présentées à partir soit de la fonction de covariance, soit de représentations intégrales. Nous étudions aussi les propriétés temporelles et spectrales du processus des accroissements. D’autre part, nous montrons que (presque) tous les mBfm peuvent être atteints comme la limite (au sens de la convergence faible) des sommes partielles de processus (super)linéaires. Enfin, un algorithme de simulation exacte est présenté et quelques simulations illustrent les propriétés du mBfm.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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