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Journal of Theoretical Probability

, Volume 21, Issue 3, pp 586–603 | Cite as

Finitely Additive Supermartingales

  • Gianluca Cassese
Article

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.

Keywords

Bichteler–Dellacherie theorem Conditional expectation Doléans-Dade measure Doob–Meyer decomposition Finitely additive measures Supermartingales Yosida–Hewitt decomposition 

Mathematics Subject Classification (2000)

28A12 60G07 60G20 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Università del SalentoLecceItaly
  2. 2.University of LuganoLuganoSwitzerland

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