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

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.

Domaines: Probabilités [math.PR]

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, 2006, 343, pp.767-772. ⟨hal-00652070⟩