Definition 1.2.2 (Progressively Measurable Random Differential Operator). Let $(\Omega, \cf, \bp)$ be a filtered probability space and $L = \sum_{|\alpha| \le k}a_{\alpha}$ be a random differential operator on $\Omega$, then $L$ is progressively measurable with respect to $\bracs{\mathcal{F}_t}$ if for each $\alpha \in \nat_{0}$ with $|\alpha| \le k$, $a_{\alpha}: [s, \infty) \times \Omega \to \real$ is progressively measurable with respect to $\bracs{\mathcal{F}_t}$.