an:02120315
Zbl 1053.60514
Selivanov, A. V.
On time changes for L??vy processes
EN
Russ. Math. Surv. 58, No. 2, 388-389 (2003); translation from Usp. Mat. Nauk 58, No. 2, 175-176 (2003).
00099462
2003
j
60G51 60G30
Let \(Z\) be a L??vy process and let \(Y\) be a nondecreasing c??dl??g 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 \(({\mathcal F}_t)_{t\geq0}\).
Zdzis??aw Rychlik (Lublin)