# Predictable process

In stochastic analysis, a part of the mathematical theory of probability, a **predictable process** is a stochastic process whose value is knowableTemplate:Clarify at a prior time. The predictable processes form the smallest classTemplate:Clarify that is closed under taking limits of sequences and contains all adapted left-continuous processesTemplate:Clarify.

## Mathematical definition

### Discrete-time process

Given a filtered probability space , then a stochastic process is *predictable* if is measurable with respect to the σ-algebra for each *n*.^{[1]}

### 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.^{[2]}

## Examples

- Every deterministic process is a predictable process.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=

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- Every continuous-time process that is left continuous is a predictable process.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=

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