  Subordinating a random walk to a renewal process yields a continuous time
random walk (CTRW) model for diffusion, including the possibility of anomalous
diffusion. Transition densities of scaling limits of power law CTRWs have been
shown to solve fractional Fokker-Planck equations. We consider limits of
sequences of CTRWs which arise when both waiting times and jumps are taken from
an infinitesimal triangular array. We identify two different limit processes
$X_t$ and $Y_t$ when waiting times precede or follow jumps, respectively. In
the limiting procedure, we keep track of the renewal times of the CTRWs and
hence find two more limit processes. Finally, we calculate the joint law of all
four limit processes evaluated at a fixed time $t$.
