Definition:Adapted Stochastic Process/Discrete Time

Definition
Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \mathop \in \N}, \Pr}$ be a filtered probability space.

Let $\sequence {X_n}_{n \mathop \in \N}$ be a sequence of real-valued random variables.

We say that $\sequence {X_n}_{n \mathop \in \N}$ is an adapted stochastic process :


 * $X_n$ is $\FF_n$-measurable random variable for each $n \in \N$.