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.
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