In this talk I will present the results of a recent project. The motivation for this project was to find a method for simulating positive self-similar Markov processes (pssMp). Any pssMp can be represented as the exponential of a Lévy process subjected to a random time change. Based on discrete observations of this Lévy process we were able to define an approximation of the pssMp and provide a limit theorem for the scaled discretization error.

I will attempt to appeal to a broad audience by staying away from technical details. Instead I will showcase some of the limit theory through simulations.