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On time changes for Lévy processes. (English. Russian original) Zbl 1053.60514
Russ. Math. Surv. 58, No. 2, 388-389 (2003); translation from Usp. Mat. Nauk 58, No. 2, 175-176 (2003).
Let $$Z$$ be a Lévy process and let $$Y$$ be a nondecreasing càdlàg process independent of $$Z$$. Define $$X:= Z\circ\tau$$, i.e., $$X_t=Z_{\tau_t}, t\geq0$$.
The author presents conditions under which the measure $$\widetilde{P}:=\text{Law}(X_t,t\geq 0)$$ is locally absolutely continuous with respect to the measure $$P:=\text{Law}(Y_t,t\geq0).$$ These measures are considered on the Skorokhod space $$D(\mathbb{R}_{+})$$ with canonical filtration $$({\mathcal F}_t)_{t\geq0}$$.
MSC:
 60G51 Processes with independent increments; Lévy processes 60G30 Continuity and singularity of induced measures
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