Definition:Filtered Probability Space/Discrete Time

Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\sequence {\mathcal F_n}_{n \mathop \in \N}$ be a discrete-time filtration of $\Sigma$.

We say that $\struct {\Omega, \Sigma, \sequence {\mathcal F_n}_{n \mathop \in \N}, \Pr}$ is a filtered probability space.

Sources

• 1991: David Williams: Probability with Martingales ... (previous) ... (next): $10.1$: Filtered Spaces