Geodesic
The measure preserving and nonsingular
Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 144-154.

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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 conditions on the Lévy measure of the process, we construct the group of ${\mathcal P}_\xi$ – preserving transformations of ${\mathbb D}[0, 1].$ For the Lévy process that has only positive (or only negative) jumps, we construct the semigroup of nonsingular transformations. 
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Natalya V. Smorodina. The measure preserving and nonsingular. Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 144-154. http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a14/

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