Abstract
On the real line, there exist $\sigma$-finite measures which are not Radon measures, but are nevertheless defined on all bounded intervals $\big(\text{e.g.} \frac{1}{x} \sin \frac{1}{x} dx, \text{or} \sum_n\frac{(-1)^n}{n} \delta_{1/n}\big).$ Similarly, in stochastic calculus, there exist processes that, though not semimartingales, can be obtained as stochastic integrals of predictable processes with respect to semimartingales. This paper deals with such processes.
Citation
M. Emery. "A Generalization of Stochastic Integration with Respect to Semimartingales." Ann. Probab. 10 (3) 709 - 727, August, 1982. https://doi.org/10.1214/aop/1176993779
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