A continuous semimartingale is a process $(S_{t})_{t\ge 0}$ s.t. $$S_{t}=S_{0}+M_{t}+A_{t}\quad\forall t\ge 0$$where 1. $S_{0}$ is $\mathcal{F}_{0}$-measurable 2. $(M_{t})_{t\ge 0}$ is a continuous local martingale s.t. $M_{0}=0$ 3. $(A_{t})_{t\ge 0}$ is a continuous adapted process of Variation s.t. $A_{0}=0$