  In a continuous time random walk (CTRW), each random jump follows a random
waiting time. CTRW scaling limits are time-changed processes that model
anomalous diffusion. The outer process describes particle jumps, and the
non-Markovian inner process (or time change) accounts for waiting times between
jumps. This paper studies fractal properties of the sample functions of a
time-changed process, and establishes some general results on the Hausdorff and
packing dimensions of its range and graph. Then those results are applied to
CTRW scaling limits.
