Representation Formula for Viscosity Solutions to Parabolic PDEs with Sublinear Operators

2019/07/16 by Marco Pozza, Pozza, Marco
Economics, Econometrics and Finance · Engineering · Mathematics · #35K55 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1907.07104

openalex publication_date 2019/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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