On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations

The classical Feynman–Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing representations for solutions of linear Kolmogorov PDEs. This opens the door derivation sampling based Monte Carlo approximation methods, which can be meshfree thereby stand chance to approximate PDEs without suffering from curse dimensionality. In this paper, we extend formula certain semilinear More specifically, identify suitable fixed point (SFPEs), arise when is formally applied Kolmorogov PDEs, as viscosity corresponding justifies, in particular, employing full-history recursive multilevel Picard (MLP) algorithms, have recently been shown overcome dimensionality numerical SFPEs,