  The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and
under power law regime is splitted into three distinct random walks: (rw_1), a
random walk along the line of natural time, happening in operational time;
(rw_2), a random walk along the line of space, happening in operational
time;(rw_3), the inversion of (rw_1), namely a random walk along the line of
operational time, happening in natural time. Via the general integral equation
of CTRW and appropriate rescaling, the transition to the diffusion limit is
carried out for each of these three random walks. Combining the limits of
(rw_1) and (rw_2) we get the method of parametric subordination for generating
particle paths, whereas combination of (rw_2) and (rw_3) yields the
subordination integral for the sojourn probability density in space-time
fractional diffusion.
