Radon-Nikodym density martingale
= Radon-Nikodym density martingale
{c}
{title2=$Z_t=\mathbb E_{\mathbb P}[d\mathbb Q/d\mathbb P\mid\mathcal F_t]$}
For an absolutely continuous change of probability measure, restricting its <Radon-Nikodym derivative> to the current sigma-algebra gives this nonnegative uniformly integrable <martingale>. If $Z_T>0$ almost surely, the measures are equivalent on $\mathcal F_T$. This finite-horizon equivalence need not imply equivalence on a larger sigma-algebra.