In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process 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.
[clarification needed] Given a filtered probability space
, then a stochastic process
is measurable with respect to the σ-algebra
for each n.[1] Given a filtered probability space
, then a continuous-time stochastic process
, considered as a mapping from
, is measurable with respect to the σ-algebra generated by all left-continuous adapted processes.