I'm having trouble understanding the concept of a previsible process in continuous time, so I'm asking this question to get a better idea of what it means for a process to be previsible.
(In what follows, suppose we're working with respect to a fixed filtered probability space.)
We say a process $H$ is previsible if $H$ is $\mathcal{P}$-measurable, where $\mathcal{P}$ is the $\sigma$-algebra generated by events of the form $E\times(s,t]$, where $E\in\mathcal{F}_s$ and $t>s$.
We can easily show that for any previsible process $H$, $H_t$ is $\sigma(\mathcal{F}_s:s
Thank you.