  We study some jumping SDE and the corresponding Fokker-Planck (or Kolmogorov
forward) equation, which is a non-local PDE. We assume only some measurability
and growth conditions on the coefficients. We prove that for any weak solution
$(f_t)_{t\in [0,T]}$ of the PDE, there exists a weak solution to the SDE of
which the time marginals are given by $(f_t)_{t\in[0,T]}$. As a corollary, we
deduce that for any given initial condition, existence for the PDE is
equivalent to weak existence for the SDE and uniqueness in law for the SDE
implies uniqueness for the PDE. This extends some ideas of Figalli [5]
concerning continuous SDEs and local PDEs.
