The measure preserving and nonsingular transformations of the jump Levy processes

Abstract

Let ξ(t), t belongs [0, 1], be a jump Levy process. By Pξ, we denote the law of ξ in the Skorokhod space D[0, 1]. Under some conditions on the Levy measure of the process, we construct the group of Pξ preserving transformations of D[0, 1]. For the Levy process that has only positive (or only negative) jumps, we construct the semigroup of nonsingular transformations.