Numerical Simulation of Decoupled Continuous-Time Random Walks with Superheavy-Tailed Waiting Time Distributions

We develop a numerical method to study the long-time behavior of continuous-time random walks characterized by superheavy-tailed distributions of waiting times. To test the method, we consider symmetric jump-length distributions with both finite second moments and heavy tails for which the asymptotic behavior of the walking particle is known exactly. Our numerical results for the distributions of the particle position are in excellent agreement with the analytical ones.