  Einstein's explanation of Brownian motion provided one of the cornerstones
which underlie the modern approaches to stochastic processes. His approach is
based on a random walk picture and is valid for Markovian processes lacking
long-term memory. The coarse-grained behavior of such processes is described by
the diffusion equation. However, many natural processes do not possess the
Markovian property and exhibit to anomalous diffusion. We consider here the
case of subdiffusive processes, which are semi-Markovian and correspond to
continuous-time random walks in which the waiting time for a step is given by a
probability distribution with a diverging mean value. Such a process can be
considered as a process subordinated to normal diffusion under operational time
which depends on this pathological waiting-time distribution. We derive two
different but equivalent forms of kinetic equations, which reduce to know
fractional diffusion or Fokker-Planck equations for waiting-time distributions
following a power-law. For waiting time distributions which are not pure power
laws one or the other form of the kinetic equation is advantageous, depending
on whether the process slows down or accelerates in the course of time.
