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.
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⟩
