Definition:Filtration of Sigma-Algebra/Discrete Time
Jump to navigation
Jump to search
Definition
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\sequence {\FF_n}_{n \mathop \in \N}$ be an sequence of sub-$\sigma$-algebras of $\Sigma$.
That is:
- $\FF_i \subseteq \FF_j$ whenever $i \le j$.
We say that $\sequence {\FF_n}_{n \mathop \in \N}$ is a filtration of $\Sigma$.
Sources
- 1991: David Williams: Probability with Martingales ... (previous) ... (next): $10.1$: Filtered Spaces