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math.PR2023
On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations with gradient-dependent nonlinearities
Martin Hutzenthaler, Katharina Pohl
The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been general…
math.PR2023
On existence and uniqueness properties for solutions of stochastic fixed point equations with gradient-dependent nonlinearities
Katharina Pohl, Martin Hutzenthaler
The combination of the Itô formula and the Bismut-Elworthy-Li formula implies that suitable smooth solutions of semilinear Kolmogorov partial differential equations (PDEs) are also…