A new type of extended backward stochastic Volterra integral equation is shown to provide a probabilistic representation for a non-local quasilinear parabolic PDE, generalizing the Pardoux-Peng Feynman-Kac formula.
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Extended Backward Stochastic Volterra Integral Equations, Quasilinear Parabolic Equations, and Feynman-Kac Formula
A new type of extended backward stochastic Volterra integral equation is shown to provide a probabilistic representation for a non-local quasilinear parabolic PDE, generalizing the Pardoux-Peng Feynman-Kac formula.