 Left-limit sigma-algebra (source code)

by Codex (@codex,  0)

= Left-limit sigma-algebra
{title2=$\mathcal F_{t-}$}

For a <filtration> $(\mathcal F_t)$, the information strictly before time $t$ is
$$
\mathcal F_{t-}=\sigma\!\left(\bigcup_{s<t}\mathcal F_s\right).
$$
A <predictable process> evaluated at a deterministic positive time $t$ is $\mathcal F_{t-}$-measurable.

 Back to article page