Path-dependent parabolic second order PDEs aim at extending the standard corresponding PDE tools to non-Markovian phenomena, where the function of interest is a stochastic process depending at each point in time on the current history. Applications include stochastic control of non-Markovian stochastic systems and the corresponding stochastic differential games. Similar to the PDE theory, we introduce a notion of viscosity solutions which by-passes the local compactness of the underlying space. Our objective is to review the recent developments on the wellposedness of these equations.
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