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

2006/07/22 by Erick Herbin, Herbin, Erick, Ely Merzbach +1
Mathematics · #60G15 #60G17 #60G18 #62G05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G15 #msc:60G17 #msc:60G18 #msc:62G05

paper · pdf · doi:10.48550/arxiv.math/0607575

6 pages

arxiv created 2006/07/22 · arxiv updated 2009/12/01

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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