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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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