  The purpose of this paper is to investigate the long time behaviour for a
self-interacting diffusion and a self-interacting velocity jump process. While
the diffusion case has already been studied for some particular potential
function, the second one, which belongs to the family of piecewise
deterministic processes, is new.
  Depending on the underlying potential function's shape, we prove either the
almost sure convergence or the recurrence for a natural extended process given
by a change a variable.
