Adapted process

In the study of stochastic processes, a stochastic process is adapted (also referred to as a non-anticipating or non-anticipative process) if information about the value of the process at a given time is available at that same time. An informal interpretation^[1] is that X is adapted if and only if, for every realisation and every n, X_n is known at time n. The concept of an adapted process is essential, for instance, in the definition of the Itō integral, which only makes sense if the integrand is an adapted process.