### THE MEASURE PRESERVING AND NONSINGULAR TRANSFORMATIONS OF THE JUMP LÉVY PROCESSES

**NATALYA V. SMORODINA**

*Theory of Stochastic Processes*

*Vol. 14 (30), no. 1, 2008, pp. 144–154*

Let $\xi(t), t\in[0,1]$ be a jump L\'evy process. By $\Cal P_\xi$, we denote the law of $\xi$ in the Skorokhod space $\Bbb D[0,1].$ Under some conditions on the L\'evy measure of the process, we construct the group of $\Cal P_\xi-$ preserving transformations of $\Bbb D[0,1].$ For the L\'evy process that has only positive (or only negative) jumps, we construct the semigroup of nonsingular transformations.

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