A characterization of the set-indexed fractional Brownian motion by increasing paths

Erick Herbin; Ely Merzbach

doi:10.1016/j.crma.2006.11.009

A characterization of the set-indexed fractional Brownian motion by increasing paths

Erick Herbin
, Ely Merzbach

Department of Mathematics

Dassault Aviation

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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. To cite this article: E. Herbin, E. Merzbach, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Original language	English
Pages (from-to)	767-772
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	343
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2006.11.009
State	Published - Dec 2006

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10.1016/j.crma.2006.11.009

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AB - 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).

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A characterization of the set-indexed fractional Brownian motion by increasing paths

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