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Set-indexed Brownian Motion on Increasing Paths |
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| Authors: | Ely Merzbach Arthur Yosef |
| Institution: | 1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel |
| 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. |
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