Geodesic
Decomposition of optional supermartingales
Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 145-158

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Let $X=(X_t, \mathscr F_t)$ be an optional submartingale of the class $(D)$. It is proved that there exist an optional martingale $m=(m_t, \mathscr F_t)$ and a strongly predictable process $A=(A_t, \mathscr F_t)$ such that the Doob decomposition $X_t=m_t+A_t$ is valid. Bibliography: 10 titles. 
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     author = {L. I. Gal'chuk},
     title = {Decomposition of optional supermartingales},
     journal = {Sbornik. Mathematics},
     pages = {145--158},
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     number = {2},
     year = {1982},
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     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_2_a0/}
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L. I. Gal'chuk. Decomposition of optional supermartingales. Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 145-158. http://geodesic.mathdoc.fr/item/SM_1982_43_2_a0/