Geodesic
On the conditions of the uniform integrability of the continuous nonnegative martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 821-825 
A. A. Novikov. On the conditions of the uniform integrability of the continuous nonnegative martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 821-825. http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a11/
@article{TVP_1979_24_4_a11,
     author = {A. A. Novikov},
     title = {On the conditions of the uniform integrability of the continuous nonnegative martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {821--825},
     year = {1979},
     volume = {24},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the uniform integrability of martingales $$ Z_t=\exp\{\mu_t-1/2\langle\mu\rangle_t\} $$ is considered, where $\mu_t$ is a continuous martingale and $\langle\mu\rangle_t$ is its increasing process. It is shown that the condition $$ \mathbf M\exp\{1/2\langle\mu\rangle_{\infty}-C\langle\mu\rangle_{\infty}^{1/2}\}<\infty $$ with any positive constant $C$ implies the uniform integrability of $Z_t$. In the case when $\mu_t$ is a stopped Wiener process the another condition (which is weaker and nonimproved in some sence) is given.