Geodesic
Decomposition of optional supermartingales
Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 145-158 
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/
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     title = {Decomposition of optional supermartingales},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Meier P. A., Veroyatnost i potentsialy, Mir, M., 1973

[2] Dellacherie C., Deux remarques sur la séparabilité optionnelle, Sem. Prob. (Strasbourg, XL), Lecture Notes in Math., 581, Springer-Verlag, Berlin, 1977 | MR

[3] Dellacherie C., Sur la régularisation des surmartingales, Sem. Prob. (Strasbourg, XL), Lecture Notes in Math, 581, Springer-Verlag, Berlin, 1977 | MR

[4] Dellacherie C., Meyer P. A., Un nouveau théorème de projection et de section, Sem. Prob. (Strasbourg, IX), Lecture Notes in Math., 465, Springer-Verlag, Berlin, 1975 | MR

[5] Galchuk L. I., “O suschestvovanii optsionalnykh modifikatsii dlya martingalov”, Teoriya veroyatn., XXII:3 (1977), 620–622

[6] Dellacherie C., Meyer P. A., Probabilités et potentiels (version refondue), Hermann, Paris, 1976 | MR

[7] Neveu J., Martingales á temps discret, Masson, Paris, 1972 | MR

[8] Dellasheri K., Emkosti i sluchainye protsessy, Mir, M., 1975 | MR

[9] Galchuk L. I., “Optsionalnye martingaly”, Matem. sb., 112 (154) (1980), 483–521 | MR

[10] Jacod J., “Multivariate point process: predictable projection, Radon–Nicodym derivatives, representation of martingales”, Z. W-theorie, 31:3 (1975), 235–253 | MR | Zbl