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Let $B$ be a standard brownian motion and $$ X_t=\int_0^t B_s \, ds. $$ What is the quadratic variation $[X]_t$ of $X$?

I see $dX_t$ as an sde with drift term $B_t$.

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up vote 2 down vote accepted

$[X]=0$ since $X$ has finite variation.

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