2023/10/27 by Martin Hutzenthaler, Hutzenthaler, Martin, Katharina Pohl +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fractional Differential Equations Solutions #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2310.18197
openalex publication_date 2023/10/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28
The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been generalized to nonlinear partial differential equations on the one hand via backward stochastic differential equations and on the other hand via stochastic fixed-point equations. In this article we generalize the representation via stochastic fixed-point equations to allow the nonlinearity in the semilinear partial differential equation to depend also on the gradient of the solution.