A few comments on a result of A. Novikov and Girsanov's theorem

Abstract

We give a simple proof that for a continuous local martingale $M_{t}$ $$ \liminf_{\varepsilon\downarrow0}\varepsilon \log Ee^{(1-\varepsilon) \langle M\rangle_{\infty}/2}<\infty \Longrightarrow E\exp(M_{\infty}-\langle M\rangle_{\infty}/2)=1. $$