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.
Given a filtered probability space , then a stochastic process is predictable if is measurable with respect to the σ-algebra for each n.
Given a filtered probability space , then a continuous-time stochastic process is predictable if , considered as a mapping from , is measurable with respect to the σ-algebra generated by all left-continuous adapted processes. This ÃÂ-algebra is also called the predictable ÃÂ-algebra.