Martingales on Random Sets and the Strong Martingale Property

@inproceedings{Sharpe2000MartingalesOR,
  title={Martingales on Random Sets and the Strong Martingale Property},
  author={Michael J. Sharpe},
  year={2000}
}
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 to Λ 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… CONTINUE READING

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