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VIII: 17, 310-315, LNM 381 (1974)
MEYER, Paul-André
Une représentation de surmartingales (Martingale theory)
Garsia asked whether every right continuous positive supermartingale $(X_t)$ bounded by $1$ is the optional projection of a (non-adapted) decreasing process $(D_t)$, also bounded by $1$. This problem is solved by an explicit formula, and a proof is sketched showing that, if boundedness is not assumed, the proper condition is $D_t\le X^{*}$
Comment: The ``exponential formula'' appearing in this paper was suggested by a more concrete problem in the theory of Markov processes, using a terminal time. Similar looking formulas occurs in multiplicative decompositions and in 801. For the much more difficult case of positive submartingales, see 1023 and above all Azéma, Z. für W-theorie, 45, 1978 and its exposition 1321
Keywords: Supermartingales, Multiplicative decomposition
Nature: Original
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