Large deviations for generalized backward stochastic differential equations

TL;DR

This paper establishes large deviation principles for generalized backward stochastic differential equations coupled with reflecting diffusion processes, linking stochastic analysis with PDE boundary conditions.

Contribution

It introduces the first large deviation results for these coupled equations under weak monotonicity, extending stochastic and PDE theory.

Findings

Large deviation principle for reflecting SDEs established.

Large deviation principle for generalized backward SDEs proved.

Derived limit results for nonlinear Neumann boundary PDEs.

Abstract

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential equations with reflecting boundaries under weak monotonicity conditions. Then based on the obtained result and the contraction principle, the large deviation principle for the generalized backward stochastic differential equations is proved. As a by-product, we obtain a limit result about parabolic partial differential equations with the nonlinear Neumann boundary conditions.