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.
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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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Ivanoff, B.G., Merzbach, E. A martingale characterization of the set-indexed Brownian motion. J Theor Probab 9, 903–913 (1996). https://doi.org/10.1007/BF02214256
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DOI: https://doi.org/10.1007/BF02214256