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How to make this heuristic extension of Itô-Tanaka's formula valid
Here is my story, I have the following function :
$$
g(x)=(1+x)\cdot\exp\left(-\frac{(\log(x+a)+c)^2}{2\sigma^2}\right)1[x\ge y]=f(x)\cdot1[x\ge y]
$$
with $a,c,\sigma$ being "good" reals so that ...
