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Stochastic integrals with respect to optional semimartingales and random measures

L. I. Gal'čuk

Moscow

Abstract: 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.

Received: 16.02.1981

 English version: Theory of Probability and its Applications, 1985, 29:1, 93–108

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