A martingale characterization of the set-indexed Brownian motion |
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| Authors: | B Gail Ivanoff Ely Merzbach |
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| Institution: | (1) Department of Mathematics and Statistics, University of Ottowa, KIN 6N5 Ottowa, Ontario, Canada;(2) Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel |
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| Abstract: | We characterize a Brownian motion indexed by a semilattice of sets, using the theory of set-indexed martingales: a square integrable continuous set-indexed strong martingale is a Brownian motion if and only if its compensator is deterministic and continuous.Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.Research done while this author was visiting the University of Ottawa. He wishes to thank Professor Ivanoff for her kind hospitality. |
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| Keywords: | Set-indexed Brownian motion lattice strong martingale compensator |
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