Geodesic
Optional martingales
Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 435-468 
L. I. Gal'chuk. Optional martingales. Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 435-468. http://geodesic.mathdoc.fr/item/SM_1981_40_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is proved that every optional local martingale $X$ is representable in the form $X=X^g+X^c+X^d$, where $X^c$ is a continuous martingale, $X^d$ is right continuous and $X^g$ is left continuous. The paper also contains results concerning square-integrable martingales. In paticular, a definition of stochastic integrals with respect to optional martingales is given, and a formula for change of variables is proved. Bibliography: 13 titles.

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

[4] C. Deliacherie, P. A. Meyer, Probabilités et potentiels (version refondue), Hermann, Paris, 1976

[5] K. Dellasheri, Emkosti i sluchainye protsessy, izd.-vo “Mir”, Moskva, 1975 | MR

[6] C. Deliacherie, “Remarques sur la séparabilité optionnelle”, Sem. Prob., Strasbourg, XI, Lecture Notes Math., 585, Springer-Verlag, Berlin, 1977

[7] J. Horowitz, “Optional supermartingales and the Andersen–Jessen theorem”, Z. W-theorie, 43 (1978), 263–272 | MR | Zbl

[8] J. L. Doob, “Stochastic process measurablity conditions”, Ann. Inst. Fourier, Grenoble, 25:3–4 (1975), 163–176 | MR | Zbl

[9] A. Benveniste, “Séparabilité optionnelle, d'après Doob”, Sem. Prob., Strasbourg, X, 511, Lecture Notes Math., Springer-Verlag, Berlin, 1976, 521–531 | MR

[10] P. A. Meier, Veroyatnost i potentsialy, izd-vo “Mir”, Moskva, 1973

[11] P. A. Meyer, “Un cours sur les integrales stochastiques”, Sem. Prob., Strasbourg, X, 511, Lecture Notes Math., Springer-Verlag, Berlin, 1976 | MR

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

[13] Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “Absolyutnaya nepreryvnost i singulyarnost lokalno absolyutno nepreryvnykh veroyatnostnykh raspredelenii. I; II”, Matem. sb., 107(149) (1978), 364–415 ; 108(150) (1979), 32–61 | MR | Zbl | MR | Zbl