  We propose a new kind of stochastic absolute value equations involving
absolute values of variables. By utilizing an equivalence relation to
stochastic bilinear program, we investigate the expected value formulation for
the proposed stochastic absolute value equations. We also consider the expected
residual minimization formulation for the proposed stochastic absolute value
equations. Under mild assumptions, we give the existence conditions for the
solution of the stochastic absolute value equations. The solution of the
stochastic absolute value equations can be gotten by solving the discrete
minimization problem. And we also propose a smoothing gradient method to solve
the discrete minimization problem. Finally, the numerical results and some
discussions are given.
