On the optional and orthogonal decompositions of a class of semimartingales
Abdelkarem Berkaoui
Imam Mohammed Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
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Abstract
We consider a set of probability measures, which are absolutely continuous with respect to the physical probability measure and at least one is equivalent to . We investigate necessary and sufficient conditions on , under which any -supermartingale can be decomposed into the sum of a local -martingale and a decreasing process. We also provide an orthogonal decomposition of square integrable semimartingale as the orthogonal sum of a local -martingale and a square integrable semimartingale. As one application, we state the orthogonal decomposition in an appropriate sense of the polar set of . We generalise then the results of a previous article (2021), from finite probability space and discrete time case to general continuous time case.
Cite this article
Abdelkarem Berkaoui, On the optional and orthogonal decompositions of a class of semimartingales. Port. Math. 79 (2022), no. 3/4, pp. 225–240
DOI 10.4171/PM/2083