Abstract
We show that $L^1$-bounded semimartingales (quasi-martingales, $F$-processes) correspond to finite signed measures on the $\sigma$-field of previsible sets. This representation of semimartingales as signed measures is used to derive in a unified manner the main decomposition theorems for semi- and supermartingales.
Citation
Hans Follmer. "On the Representation of Semimartingales." Ann. Probab. 1 (4) 580 - 589, August, 1973. https://doi.org/10.1214/aop/1176996887
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