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2016 A general Doob-Meyer-Mertens decomposition for g-supermartingale systems
Bruno Bouchard, Dylan Possamaï, Xiaolu Tan
Electron. J. Probab. 21: 1-21 (2016). DOI: 10.1214/16-EJP4527

Abstract

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 [36] for classical supermartingales, as well as Peng’s [41] version for right-continuous $g$-supermartingales. As examples of application, we prove an optional decomposition theorem for $g$-supermartingale systems, and also obtain a general version of the well-known dual formulation for BSDEs with constraint on the gains-process, using very simple arguments.

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Bruno Bouchard. Dylan Possamaï. Xiaolu Tan. "A general Doob-Meyer-Mertens decomposition for g-supermartingale systems." Electron. J. Probab. 21 1 - 21, 2016. https://doi.org/10.1214/16-EJP4527

Information

Received: 2 September 2015; Accepted: 25 April 2016; Published: 2016
First available in Project Euclid: 2 May 2016

zbMATH: 1343.60050
MathSciNet: MR3508683
Digital Object Identifier: 10.1214/16-EJP4527

Subjects:
Primary: 60H99

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