We have investigated the origin of cosmic radiation in terms of a sudden injection of particles in time, momentum and space. The appropriate boundary conditions for the various regions through which the particles pass were used. With all of the acceleration within a turbulent region, we find that the observed spectrum is explained by a continuous deceleration in which statistical fluctuations dominate. This is contradictory to the usual assumptions in which fluctuations do not play an important part. We find that the time dependent solution has an exponent of the power law spectrum that varies weakly with the momentum and time. The steady state solution shows the usual constant exponent.