Predictable process
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.Continuous-time process
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 σ-algebra is also called the predictable σ-algebra.Examples
