  The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their
limit processes is utilized, and the probability distributions of the bivariate
Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$
a process tracking the age, i.e. the time since the last jump. For a given CTRW
limit process $X(t)$, a sequence of discrete CTRWs in discrete time is given
which converges to $X(t)$ (weakly in the Skorokhod topology). Master equations
for the discrete CTRWs are implemented numerically, thus approximating the
distribution of $X(t)$. A consequence of the derived algorithm is that any
distribution of initial age can be assumed as an initial condition for the CTRW
limit dynamics. Four examples with different temporal scaling are discussed:
subdiffusion, tempered subdiffusion, the fractal mobile/immobile model and the
tempered fractal mobile/immobile model.
