Filtration (probability theory, $({\mathcal{F}}_t)$)

A filtration is an increasing family of sigma-algebras: ${\mathcal{F}}_s\subseteq {\mathcal{F}}_t$ whenever $s\le t$. It represents the information available as time passes.

For a filtration $({\mathcal{F}}_t)$, the information strictly before time $t$ isA predictable process evaluated at a deterministic positive time $t$ is ${\mathcal{F}}_{t-}$-measurable.