  We focus on a class of path-dependent problems which include path-dependent
(possibly Integro) PDEs, and their representation via BSDEs driven by a cadlag
martingale. For those equations we introduce the notion of decoupled mild
solution for which, under general assumptions, we study existence and
uniqueness and its representation via the afore mentioned BSDEs. This concept
generalizes a similar notion introduced by the authors in previous papers in
the framework of classical PDEs and IPDEs. For every initial condition (s,
$\eta$), where s is an initial time and $\eta$ an initial path, the solution of
such BSDE produces a couple of processes (Y s,$\eta$ , Z s,$\eta$). In the
classical (Markovian or not) literature the function u(s, $\eta$) := Y s,$\eta$
s constitutes a viscosity type solution of an associated PDE (resp. IPDE); our
approach allows not only to identify u as (in our language) the unique
decoupled mild solution, but also to solve quite generally the so called
identification problem, i.e. to also characterize the (Z s,$\eta$) s,$\eta$
processes in term of a deterministic function v associated to the (above
decoupled mild) solution u. MSC 2010 Classification. 60H30; 60H10; 35D99;
35S05; 60J35; 60J75.
