Predictable process: Difference between revisions

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Given a filtered probability space <math>(\Omega,\mathcal{F},(\mathcal{F}_t)_{t \geq 0},\mathbb{P})</math>, then a stochastic process <math>(X_t)_{t \geq 0}</math> is ''predictable'' if <math>X_{t}</math> is measureable with respect to the &sigma;-algebra <math>\mathcal{F}_{t^-}</math> for each time ''t''.{{citation needed}}
 
== PropertiesExamples ==
* Any [[deterministic system|deterministic process]] is a predictable process.
* A continuous time process which is [[left continuous]] is always a predictable process.