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

Large Deviation Principles of Obstacle Problems for Quasilinear Stochastic PDEs