Geodesic
The measure preserving and nonsingular transformations of the jump L\'evy processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 174-188

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Let $\xi(t)$, $t\in[0,1]$ be a jump Lévy process. By $\mathcal P_\xi$ we denote the law of $\xi$ in the Skorokhod space $\mathbb D[0,1]$. Under some nondegeneracy condition on the Lévy measure $\Lambda$ of the process we construct a group of a $\mathcal P_\xi$-preserving transformations of the space $\mathbb D[0,1]$. 
@article{ZNSL_2007_341_a12,
     author = {N. V. Smorodina},
     title = {The measure preserving  and nonsingular transformations of the jump {L\'evy} processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--188},
     publisher = {mathdoc},
     volume = {341},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a12/}
}
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N. V. Smorodina. The measure preserving  and nonsingular transformations of the jump L\'evy processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 174-188. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a12/