Abstract:
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.
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