Large Deviation Principles of Obstacle Problems for Quasilinear Stochastic PDEs

TL;DR

This paper establishes a large deviation principle for obstacle problems in quasi-linear stochastic PDEs, utilizing backward stochastic differential equations to provide a sufficient condition for large deviation criteria.

Contribution

It introduces a new large deviation principle for obstacle problems in quasi-linear SPDEs, expanding the theoretical framework with backward stochastic differential equations.

Findings

Large deviation principle proven for obstacle problems in quasi-linear SPDEs

Backward stochastic differential equations are key to the analysis

Provides a sufficient condition for large deviation criteria

Abstract

In this paper, we present a sufficient condition for the large deviation criteria of Budhiraja, Dupuis and Maroulas for functionals of Brownian motions. We then establish a large deviation principle for obstacle problems of quasi-linear stochastic partial differential equations. It turns out that the backward stochastic differential equations will play an important role.