Existence and convergence for stochastic differential variational inequalities

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