Set-indexed Brownian Motion on Increasing Paths

  • Ely Merzbach
  • Arthur Yosef


We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projections on all the strict increasing continuous paths are one-parameter time-change Brownian motions. We present some applications.


Set-indexed process Brownian motion Increasing path 

Mathematics Subject Classification (2000)

60G15 60G48 60G60 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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