I notice that there is a lemma: $d(XY)=XdY+YdX+d[X,Y]$ and $XY-[X,Y]$ is a martingale. I wonder how to show that $XY-[X,Y]$ is a martingale? And it is true that $[X,Y]=0$ if $X$ and $Y$ are independent?
2026-04-08 02:29:25.1775615365
Martingale and Ito lemma
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