# Predictable random process

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 $\mathbf F=(\mathcal F_t)_t$.