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

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

2006-07-22

arxiv.org/abs/math/0607575v1

Mathematics

Probability

6 pages

Scientific paper

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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