= Ornstein-Uhlenbeck likelihood relative to Wiener measure
{c}
{title2=$L_t=\exp\left(-\mu\int_0^t\omega_s\,d\omega_s-\frac{\mu^2}{2}\int_0^t\omega_s^2ds\right)$}
On each finite horizon the displayed <Radon-Nikodym derivative> changes <Wiener measure> into the law of $dX=dB-\mu Xdt$. Stop at coordinate magnitude n so the <Novikov condition> applies. Under each stopped tilted measure the coordinate solves the drifted equation, and the <Gronwall inequality> with the <Doob L2 maximal inequality> bounds its maximal second moment uniformly in n. The probability of reaching n therefore tends to zero; this proves that the unstopped density has expectation one. No unrestricted large-time Novikov estimate is needed.
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