Geodesic
Optional martingales
Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 435-468 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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