Predictable Increasing Processes

Abstract

We have discussed predictable \(\sigma \)-field and seen the crucial role played by predictable integrands in the theory of stochastic integration. In our treatment of the integration, we have so far suppressed another role played by predictable processes. In the decomposition of semimartingales, Theorem 5.55, the process A with finite variation paths turns out to be a predictable process. Indeed, this identification played a major part in the development of the theory of stochastic integration.