Geodesic
Stochastic integrals with respect to optional semimartingales and random measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 93-107 
L. I. Gal'čuk. Stochastic integrals with respect to optional semimartingales and random measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 93-107. http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a7/
@article{TVP_1984_29_1_a7,
     author = {L. I. Gal'\v{c}uk},
     title = {Stochastic integrals with respect to optional semimartingales and random measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {93--107},
     year = {1984},
     volume = {29},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Optional semimartingales are studied when «the usual» conditions are not satisfied. The random integervalued measures generated by the jumps $X_t-X_{t-}$, $X_{t+}-X_t$ of a semimartingale $X_t$ are introduced and their compensators are defined. Stochastic integrals are constructed with respect to the optional semimartingales and the random measures. For the optional semimartingales an analogue of the Doleans equation is considered and its solution is given.