  We formulate the first order Fermi acceleration in parallel shock waves in
terms of the random walk theory. The formulation is applicable to any value of
the shock speed and the particle speed, in particular to the acceleration in
relativistic shocks, as long as large angle scattering is suitable for the
scattering process of particles. We first show that the trajectory of a
particle suffering from large angle scattering can be treated as a random walk
in a moving medium with an absorbing boundary (e.g., the shock front). We
derive an integral equation to determine the density of scattering points of
the random walk, and by solving it approximately we obtain approximate
solutions of the probability density of pitch angle at and the return
probability after the shock crossing in analytical form. These approximate
solutions include corrections of several non-diffusive effects to the
conventional diffusion approximation and we show that they agree well with the
Monte Carlo results for isotropic scattering model for any shock speed and
particle speed. Finally, we give an analytical expression of the spectral index
of accelerated particles in parallel shocks valid for arbitrary shock speed.
