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 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.
- Every deterministic process is a predictable process.
- Every continuous-time adapted process that is left continuous is obviously a predictable process.
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- "Predictable processes: properties" (PDF). Archived from the original (pdf) on March 31, 2012. Retrieved October 15, 2011.