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A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths

Erick Herbin 1, 2 Ely Merzbach 3
1 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
2 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
3 Department of Mathematics
Abstract : We prove that a set-indexed process is a set-indexed fractional Brownian motion if and only if its projections on all the increasing paths are one-parameter time changed fractional Brownian motions. As an application, we present an integral representation for such processes.
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https://hal-ecp.archives-ouvertes.fr/hal-00652070
Contributor : Erick Herbin <>
Submitted on : Wednesday, December 14, 2011 - 6:00:04 PM
Last modification on : Wednesday, July 15, 2020 - 11:10:02 AM

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Erick Herbin, Ely Merzbach. A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2006, 343, pp.767-772. ⟨hal-00652070⟩

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