Finitely Additive Supermartingales
Probability
2008-04-21 v2
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 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.
Keywords
Cite
@article{arxiv.0801.1262,
title = {Finitely Additive Supermartingales},
author = {Gianluca Cassese},
journal= {arXiv preprint arXiv:0801.1262},
year = {2008}
}