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 Doléans-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. © 2008 Springer Science+Business Media, LLC.
Cassese, G. (2008). Finitely additive supermartingales. JOURNAL OF THEORETICAL PROBABILITY, 21(3), 586-603 [10.1007/s10959-008-0164-8].
Finitely additive supermartingales
CASSESE, GIANLUCA
2008
Abstract
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 Doléans-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. © 2008 Springer Science+Business Media, LLC.
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