Representation Formula for Viscosity Solutions to Parabolic PDEs with Sublinear Operators
Marco Pozza
TL;DR
This paper introduces a representation formula for viscosity solutions of nonlinear second order parabolic PDEs with sublinear operators, extending the Feynman--Kac formula via backward stochastic differential equations.
Contribution
It develops a nonlinear extension of the Feynman--Kac formula for viscosity solutions using a dynamic programming principle and backward stochastic differential equations.
Findings
Provides a new representation formula for viscosity solutions.
Extends the Feynman--Kac formula to nonlinear PDEs.
Connects stochastic processes with nonlinear PDE theory.
Abstract
We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDE problem involving sublinear operators. This is done through a dynamic programming principle derived from [8]. The formula can be seen as a nonlinear extension of the Feynman--Kac formula and is based on the backward stochastic differential equations theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Partial Differential Equations · Stochastic processes and financial applications · Stability and Controllability of Differential Equations