Set-indexed Brownian Motion on Increasing Paths

Ely Merzbach () and Arthur Yosef ()
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Ely Merzbach: Bar-Ilan University
Arthur Yosef: Bar-Ilan University

Journal of Theoretical Probability, 2009, vol. 22, issue 4, 883-890

Abstract: Abstract 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.

Keywords: Set-indexed process; Brownian motion; Increasing path; 60G15; 60G48; 60G60 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-008-0188-0

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