= Semimartingale invariance under equivalent measures
On a fixed finite horizon, equivalent probability measures have the same <semimartingales>. For a strictly positive continuous <Radon-Nikodym density martingale> $Z$ and a continuous local martingale $L$ under the original measure, $L-\int Z^{-1}d[L,Z]$ is a local martingale under the new one, by the <Girsanov theorem>. Thus the finite-variation part of a continuous <semimartingale decomposition> changes by the opposite covariation correction.
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