Geodesic
Beneš condition for discontinuous exponential martingale
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 144-154 
R. Liptser. Beneš condition for discontinuous exponential martingale. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 144-154. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a8/
@article{ZNSL_2011_396_a8,
     author = {R. Liptser},
     title = {Bene\v{s} condition for discontinuous exponential martingale},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {144--154},
     year = {2011},
     volume = {396},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is known that the Girsanov exponent $\mathfrak z_t$, being solution of Doléans-Dade equation $\mathfrak z_t=1+\int_0^t\mathfrak z_s\alpha(s)\,dB_s$ generated by Brownian motion $B_t$ and a random process $\alpha(t)$ with $\int_0^t\alpha^2(s)\,ds<\infty$ a.s., is the martingale provided that the Beneš condition $$ |\alpha(t)|^2\le\mathrm{const.}\big[1+\sup_{s\in[0,t]}B^2_s\big],\quad\forall\ t>0, $$ holds true. In this paper, we show that $\int_0^t\alpha(s)\,dB_s$ can be replaced by a purely discontinuous square integrable martingale $M_t$ paths from the Skorokhod space $ \mathbb D_{[0,\infty)}$ having jumps $\alpha(s)\triangle M_t>-1$. The method of proof differs from the original Beneš proof.

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