  In this paper we prove a nonlocal version of the celebrated Inverse Problem
of Donsker and Varadhan~\cite{DV} for nonlocal elliptic operators of the form
$$ \cL u = L_K u + \cB_K (h,u), $$ where $L_K$ is a uniformly elliptic nonlocal
operator with smooth coefficients, and, for $h:\R^N \to \R$ smooth and bounded,
$\cB_K(h,u)$ is the associated bilinear form, which can be regarded as a
nonlocal transport term.
