Limit Theorems for Stochastic Variational Inequalities with Non-Lipschitz Coefficients

We establish various limit theorems for one-dimensional stochastic variational inequalities with Yamada-Watanabe type conditions on the coefficients, including, the construction of the solution through the Euler scheme, the convergence of the Yosida approximation and stability of the solution. Besides, convergence rates are presented for these two approximations when the coefficients are only Hölder continuous.