Symmetry Analysis of Semi-Linear Partial Differential Equations and Forward Backward Stochastic Differential Equations

TL;DR

This paper explores the Lie symmetries of semi-linear PDEs and their relation to symmetries of FBSDEs, using the generalized Feynman-Kac formula to establish connections between these mathematical structures.

Contribution

It introduces a novel analysis linking symmetries of semi-linear PDEs with those of FBSDEs via the generalized Feynman-Kac formula.

Findings

Identifies symmetry structures of semi-linear PDEs.

Establishes correspondence between PDE symmetries and FBSDE symmetries.

Provides a framework for symmetry analysis in stochastic differential equations.

Abstract

We examine the Lie symmetries of a semi-linear partial differential equations and their connections to the analogous symmetries of the forward-backward stochastic differential equations (FBSDEs), established through the generalized Feynman-Kac formula.