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Finitely Additive Supermartingales

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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.

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Author notes

  1. Gianluca Cassese

    Present address: Dipartimento di Scienze Economiche e Matematico-Statistiche, Ecotekne, via per Monteroni, 73100, Lecce, Italy

Authors and Affiliations

  1. Università del Salento, Lecce, Italy

    Gianluca Cassese

  2. University of Lugano, Lugano, Switzerland

    Gianluca Cassese

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  1. Gianluca Cassese
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Correspondence to Gianluca Cassese.

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I am indebted to an anonymous referee for several helping suggestions.

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Cassese, G. Finitely Additive Supermartingales. J Theor Probab 21, 586–603 (2008). https://doi.org/10.1007/s10959-008-0164-8

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  • DOI: https://doi.org/10.1007/s10959-008-0164-8

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