Dealing with Itô, it simplifies a lot if you have terms which are continuous and of finite variation, since these terms have zero quadratic variation. I know that every increasing function has finite variation. But I have some troubles to argue why the following processes should be of finite variation. Suppose we have a predictable process $X_t$, why are the following two processes of finite variation?
- $\int_0^t X_s ds$
If $X_s$ would be positive, then everything is clear. But this must not be the case. So why are these processes of finite variation?