Geodesic
The measure preserving transformations of the jump L\'evy process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 130-140

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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 $\mathbb D[0,1]$. Bibl. – 10 titles. 
@article{ZNSL_2009_368_a9,
     author = {S. S. Gribkova},
     title = {The measure preserving transformations of the jump {L\'evy} process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {130--140},
     publisher = {mathdoc},
     volume = {368},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a9/}
}
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S. S. Gribkova. The measure preserving transformations of the jump L\'evy process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 130-140. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a9/