Finitely Additive Supermartingales |
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| Authors: | Gianluca Cassese |
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| Institution: | (1) Università del Salento, Lecce, Italy;(2) University of Lugano, Lugano, Switzerland;(3) Present address: Dipartimento di Scienze Economiche e Matematico-Statistiche, Ecotekne, via per Monteroni, 73100 Lecce, Italy |
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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.
I am indebted to an anonymous referee for several helping suggestions. |
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| Keywords: | Bichteler– Dellacherie theorem Conditional expectation Doléans-Dade measure Doob– Meyer decomposition Finitely additive measures Supermartingales Yosida– Hewitt decomposition |
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