Continuous-time random walks on bounded domains.

A useful perspective to take when studying anomalous diffusion processes is that of a continuous-time random walk and its associated generalized master equation. We derive the generalized master equations for continuous-time random walks that are restricted to a bounded domain and compare numerical solutions with kernel-density estimates of the probability-density function computed from simulations. The numerical solution of the generalized master equation represents a powerful tool in the study of continuous-time random walks on bounded domains.