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Mouvement Brownien Fractionnaire, applications aux télécommunications. Calcul Stochastique relativement à des processus fractionnaires.

Abstract : The fractional Brownian motion (fBm) has become a key process as soon as one wants to free oneself from the Markov and independence of increments properties. We have given the main properties of this process and we have insisted on certain aspects of its use as fluid queue model. Then, we have developed construction of an anticipative integral with respect to fBm from an anticipative integral with respect to the Brownian motion. Then, we have introduced an anticipative integral with respect to filtered Poisson process (fPp) from an anticipative integral with respect to marked Poisson process, an integral that we have connected to the Stieltjès integral. Our study has gone on with an Itô formula for cylindrical functional and a Hölder continuity theorem for integrated processes. To conclude, a weak convergence theorem for a sequence of fPp to a Volterra Process has been established.
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https://tel.archives-ouvertes.fr/tel-00003407
Contributor : Nicolas Savy <>
Submitted on : Monday, September 22, 2003 - 6:23:53 PM
Last modification on : Thursday, January 7, 2021 - 4:24:07 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 10:35:10 AM

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  • HAL Id : tel-00003407, version 1

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Nicolas Savy. Mouvement Brownien Fractionnaire, applications aux télécommunications. Calcul Stochastique relativement à des processus fractionnaires.. Mathématiques [math]. Université Rennes 1, 2003. Français. ⟨tel-00003407⟩

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