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A general Doob-Meyer-Mertens decomposition for g-supermartingale systems
Electronic Journal of Probability
We provide a general Doob-Meyer decomposition for g-supermartingale systems, which does not require any right-continuity on the system, nor that the filtration is quasi left-continuous. In particular, it generalizes the Doob-Meyer decomposition of Mertens  for classical supermartingales, as well as Peng's  version for right-continuous g-supermartingales. As examples of application, we prove an optional decomposition theorem for g-supermartingale systems, and also obtain a generaldoi:10.1214/16-ejp4527 fatcat:l64vcie5abaf5c2krfz3wzcc2y