Existence and convergence for stochastic differential variational inequalities

In this paper, we consider a class of stochastic differential variational inequalities (for short, SDVIs) consisting of an ordinary differential equation and a stochastic variational inequality. The existence to SDVIs are established under the assumption that the leading operator in the stochastic variational inequality is $P$-function and $P_0$ -function, respectively. Then, by using the sample average approximation and time stepping methods, two approximated problems corresponding to SDVIs are introduced and convergence results are obtained.