Representation Formula for Viscosity Solution to a PDE Problem involving Pucci's Extremal Operator
Marco Pozza
TL;DR
This paper derives a representation formula for viscosity solutions of elliptic PDEs with Pucci's extremal operators, extending the Feynman-Kac formula through a dynamic programming approach.
Contribution
It introduces a nonlinear representation formula for viscosity solutions involving Pucci's operators, based on a dynamic programming principle.
Findings
Provides a new representation formula for viscosity solutions.
Extends the Feynman-Kac formula to nonlinear elliptic PDEs.
Connects PDE solutions with stochastic control via dynamic programming.
Abstract
We provide a representation formula for viscosity solutions to an elliptic Dirichlet problem involving Pucci's extremal operators. This is done through a dynamic programming principle derived from Denis, Hu and Peng (2010). The formula can be seen as a nonlinear extension of the Feynman-Kac formula.
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