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August, 1984 Synonymity, Generalized Martingales, and Subfiltration
Douglas N. Hoover
Ann. Probab. 12(3): 703-713 (August, 1984). DOI: 10.1214/aop/1176993221


Aldous recently introduced the notion of synonymity of stochastic processes, a notion of equivalence for processes on a stochastic basis which generalizes the notion of "having the same distribution". We show that generalized martingale properties, such as the semimartingale property, are preserved under synonymity, and that synonymous semimartingales have decompositions with the same distribution law. A variation of our method yields a relatively elementary proof of the theorem of Stricker that semimartingale remains a semimartingale with respect to any subfiltration to which it is adapted.


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Douglas N. Hoover. "Synonymity, Generalized Martingales, and Subfiltration." Ann. Probab. 12 (3) 703 - 713, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0545.60040
MathSciNet: MR744227
Digital Object Identifier: 10.1214/aop/1176993221

Primary: 60G07
Secondary: 60G48

Keywords: local martingale , Semimartingale , subfiltration , Synonymity

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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