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I'm currently trying to understand the proof of Itô's formula from the book of Revuz and Yor.

In the proof the integration by parts formula for continuous semimartingales is used. But to apply this I need to know that $f(X)$ is a continuous semimartingale if $X$ is a continuous semimartingale and $f$ is twice continuously differentiable.

Can you give any hint how this does hold? It would probably suffice if it holds for polynomial functions $f$.

Thanks in advance!

Conny
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  • You may be interested by a discrete version of the proof : see for that the third example in https://math.stackexchange.com/q/1774670 – Jean Marie Aug 26 '19 at 09:57
  • Thanks for your comment. But I need to understand the exact version from Revuz and Yor since I'm studying for an exam where this proof could be part of. – Conny Aug 26 '19 at 10:08

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