Predictable random process

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A stochastic process $X=(X_t(\omega),\mathcal F_t)$ that is measurable (as a mapping $(\omega,t)\to X(\omega,t)=X_t(\omega)$) with respect to the predictable sigma-algebra $\mathcal P=\mathcal P(\mathbf F)$, where $\mathbf F=(\mathcal F_t)_t$.


[a1] C. Dellacherie, P.A. Meyer, "Probabilities and potential" , B , North-Holland (1982) (Translated from French)
[a2] R.S. Liptser, A.N. Shiryaev, "Statistics of random processes" , II , Springer (1978) pp. 301ff (Translated from Russian)
[a3] R.Sh. Liptser, A.N. [A.N. Shiryaev] Shiryayev, "Theory of martingales" , Kluwer (1989) (Translated from Russian)
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Predictable random process. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article