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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?

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I found an answer - the answer is yes. Rogers and Williams page 358.

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  • $\begingroup$ What is the answer if you don’t mind me asking! $\endgroup$
    – Nate River
    Commented Jul 30, 2023 at 15:37
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    $\begingroup$ Please at least give a yes/no in the answer. Even better, you should make the answer self-contained, without relying on textbooks or contents behind paywalls etc. $\endgroup$
    – Trebor
    Commented Jul 30, 2023 at 15:40
  • $\begingroup$ @NateRiver the answer is yes. $\endgroup$
    – user479223
    Commented Jul 30, 2023 at 15:47

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