Maximum Principle for Quasilinear Stochastic PDEs with Obstacle
  We prove a maximum principle for local solutions of quasilinear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of It\^o's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary. 
Denis Laurent, Matoussi Anis and Zhang Jing
math.PR