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. To cite this article: E. Herbin, E. Merzbach, C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.
Herbin, E., & Merzbach, E. (2006). A characterization of the set-indexed fractional Brownian motion by increasing paths. Comptes Rendus Mathematique, 343(11–12), 767–772. https://doi.org/10.1016/j.crma.2006.11.009