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We focus on a class of path-dependent problems which include path-dependent(possibly Integro) PDEs, and their representation via BSDEs driven by a cadlagmartingale. For those equations we introduce the notion of decoupled mildsolution for which, under general assumptions, we study existence anduniqueness and its representation via the afore mentioned BSDEs. This conceptgeneralizes a similar notion introduced by the authors in previous papers inthe 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 ofsuch BSDE produces a couple of processes (Y s,$\eta$ , Z s,$\eta$). In theclassical (Markovian or not) literature the function u(s, $\eta$) := Y s,$\eta$s constitutes a viscosity type solution of an associated PDE (resp. IPDE); ourapproach allows not only to identify u as (in our language) the uniquedecoupled mild solution, but also to solve quite generally the so calledidentification problem, i.e. to also characterize the (Z s,$\eta$) s,$\eta$processes in term of a deterministic function v associated to the (abovedecoupled mild) solution u. MSC 2010 Classification. 60H30; 60H10; 35D99;35S05; 60J35; 60J75.

Decoupled mild solutions of path-dependent PDEs and IPDEsrepresented by BSDEs driven by cadlag martingales