  In this paper, we introduce and study a stochastic differential variational
inequality (SDVI) which consists of a stochastic differential equation and a
stochastic variational inequality. We obtain the existence and uniqueness of
the solutions for SDVI by using the iteration method and Gronwall's inequality.
Moreover, we show the convergence of Euler scheme for solving SDVI under some
mild conditions. Finally, we apply the obtained results to solve the electrical
circuits with diodes and the collapse of the bridge problems in stochastic
environment.
