Geodesic
The measure preserving and nonsingular transformations of the jump Lévy processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 174-188 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathbb D[0,1]$. 
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N. V. Smorodina. The measure preserving and nonsingular transformations of the jump Lévy 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/

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