Before revision:  It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by adapted binomial processes, i.e., by processes with fixed size binary increments at sampling points  .
After revision:  It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by adapted binomial processes, i.e., by processes with fixed size binary increments at sampling points . Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process .