Finitely Additive Supermartingales

Details Finitely Additive Supermartingales Finitely Additive Supermartingales

2008-01-08

arxiv.org/abs/0801.1262v2

Mathematics

Probability

Scientific paper

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Dol\'{e}ans-Dade measure. We obtain versions of the Doob Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measure.

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