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LSpice
LSpice
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There is a comment to this effect in Revuz and Yor's Continuous Martingales and Brownian MotionContinuous Martingales and Brownian Motion after the proof for continuous semimartingale vector $X=(X^1,\dots,X^d)$ and $F\in C^2$ (pg 147):

Remark 1°) The differentiability properties of $F$ may be somewhat relaxed. For instance, if some of the $X^{i}$'s are of finite variation, $F$ needs only be of class $C^1$ in the corresponding coordinates; the proof goes through just the same.

There is a comment to this effect in Revuz and Yor's Continuous Martingales and Brownian Motion after the proof for continuous semimartingale vector $X=(X^1,\dots,X^d)$ and $F\in C^2$ (pg 147):

Remark 1°) The differentiability properties of $F$ may be somewhat relaxed. For instance, if some of the $X^{i}$'s are of finite variation, $F$ needs only be of class $C^1$ in the corresponding coordinates; the proof goes through just the same.

There is a comment to this effect in Revuz and Yor's Continuous Martingales and Brownian Motion after the proof for continuous semimartingale vector $X=(X^1,\dots,X^d)$ and $F\in C^2$ (pg 147):

Remark 1°) The differentiability properties of $F$ may be somewhat relaxed. For instance, if some of the $X^{i}$'s are of finite variation, $F$ needs only be of class $C^1$ in the corresponding coordinates; the proof goes through just the same.

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Josiah Park
Josiah Park
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There is a comment to this effect in Revuz and Yor's Continuous Martingales and Brownian Motion after the proof for continuous semimartingale vector $X=(X^1,\dots,X^d)$ and $F\in C^2$ (pg 147):

Remark 1°) The differentiability properties of $F$ may be somewhat relaxed. For instance, if some of the $X^{i}$'s are of finite variation, $F$ needs only be of class $C^1$ in the corresponding coordinates; the proof goes through just the same.