Representing the CGMY and Meixner Lévy processes as time changed Brownian motions

We describe the Carr–Geman–Madan–Yor (CGMY) and Meixner processes as time changed Brownian motions. The CGMY uses a time change that is absolutely continuous with respect to the one-sided stable (Y/2) subordinator while the Meixner time change is absolutely continuous with respect to the one-sided stable (1/2) subordinator. The required time changes may be generated by simulating the requisite one-sided stable subordinator and throwing away some of the jumps as described by Asmussen and Rosinski (2001).