Let $X$ be a centered semimartingale that has continuous sample paths almost surely. Is it then true that $X$ is a continuous semimartingale? Meaning that $X$ has a decomposition $X=M+V$ where $M$ is a continuous local martingale and $V$ is a continuous finite variation process?



Is a semimartingale that is continuous a continuous semimartingale?
I found an answer - the answer is yes. Rogers and Williams page 358.


