Open Access
2000 Martingales on Random Sets and the Strong Martingale Property
Michael Sharpe
Author Affiliations +
Electron. J. Probab. 5: 1-17 (2000). DOI: 10.1214/EJP.v5-57


Let $X$ be a process defined on an optional random set. The paper develops two different conditions on $X$ guaranteeing that it is the restriction of a uniformly integrable martingale. In each case, it is supposed that $X$ is the restriction of some special semimartingale $Z$ with canonical decomposition $Z=M+A$. The first condition, which is both necessary and sufficient, is an absolute continuity condition on $A$. Under additional hypotheses, the existence of a martingale extension can be characterized by a strong martingale property of $X$. Uniqueness of the extension is also considered.


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Michael Sharpe. "Martingales on Random Sets and the Strong Martingale Property." Electron. J. Probab. 5 1 - 17, 2000.


Accepted: 16 December 1999; Published: 2000
First available in Project Euclid: 7 March 2016

zbMATH: 0953.60021
MathSciNet: MR1741775
Digital Object Identifier: 10.1214/EJP.v5-57

Primary: 60J30

Keywords: martingale , random set , strong martingale property

Vol.5 • 2000
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