Predictable process

In , a part of the mathematical theory of probability, a predictable process is a whose value is knowable at a prior time. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes.

Given a filtered probability space ${\displaystyle (\Omega ,{\mathcal {F}},({\mathcal {F}}_{n})_{n\in \mathbb {N} },\mathbb {P} )}$, then a stochastic process ${\displaystyle (X_{n})_{n\in \mathbb {N} }}$ is predictable if ${\displaystyle X_{n+1}}$ is measurable with respect to the σ-algebra ${\displaystyle {\mathcal {F}}_{n}}$ for each n.

...
Wikipedia