# 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

### Continuous-time process

Given a filtered probability space ${\displaystyle (\Omega ,{\mathcal {F}},({\mathcal {F}}_{t})_{t\geq 0},{\mathbb {P} })}$, then a continuous-time stochastic process ${\displaystyle (X_{t})_{t\geq 0}}$ is predictable if ${\displaystyle X}$, considered as a mapping from ${\displaystyle \Omega \times \mathbb {R} _{+}}$, is measurable with respect to the σ-algebra generated by all left-continuous adapted processes.[2]

## Examples

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