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A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths

Erick Herbin·Ely Merzbach
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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.

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Erick Herbin, Ely Merzbach. 2006-07-22. A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths. https://arxiv.org/abs/math/0607575

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