A simple proof of a result of A. Novikov

Details A simple proof of a result of A. Novikov A simple proof of a result of A. Novikov

2002-07-01

arxiv.org/abs/math/0207013v2

Mathematics

Probability

3 pages, few glitches corrected

Scientific paper

We give simple proofs that for a continuous local martingale M_t: 1) \liminf_{\epsilon->0} \epsilon \log Ee^{(1-\epsilon) _\infty /2} < \infty ==> E\exp(M_\infty - _\infty /2) = 1, 2) \liminf_{\epsilon->0} \epsilon \log\sup_{t>=0} Ee^{(1-\epsilon)M_t/2} < \infty ==> E\exp(M_\infty - _\infty /2) = 1 .

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