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Martingales on Random Sets and the Strong Martingale Property

   
@article{EJP57,
	author = {Michael Sharpe},
	title = {Martingales on Random Sets and the Strong Martingale Property},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {5},
	year = {1999},
	keywords = {Martingale, random set, strong martingale property},
	abstract = {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.},
	pages = {no. 1, 1-17},
	issn = {1083-6489},
	doi = {10.1214/EJP.v5-57},    
        url = {http://ejp.ejpecp.org/article/view/57}}