Continuous-time random walks: Simulation of continuous trajectories

Continuous-time random walks have been developed as a straightforward generalization of classical random-walk processes. Some ten years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin equations [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. The present work is devoted to a detailed discussion of Fogedby's model and presents its application for the robust numerical generation of sample paths of continuous time random-walk processes.