A one--dimensional model for the Barkhausen effect is considered. This model
describes a motion in a random medium. The motion exhibits a stick--slip
type behaviour in the limit of small correlation length of the random medium.
However, we prove that the velocity of the limiting motion is positive almost
everywhere. For this the corresponding Fokker--Planck equation is examined. This
equation is degenerated and has a critical singularity as well as no gradient
structure. Therefore, the proof relies mainly on choosing the right test functions,
which gives natural boundary conditions in the limit.