The authors consider the expected residual minimization method (ERM) for solving stochastic linear complementarity problems
This problem is transformed to a minimization problem . The study is based on the concept of stochastic matrices. It is shown, that the ERM problem is solvable for any if and only if is a stochastic matrix. The differentiability of is analysed under a certain strict complementarity condition with probability one. Necessary an sufficient optimality conditions for a solution are given together with error bounds. Finally the authors report on experiments for solving ERM numerically. The stochastic complementarity concept is applied to a traffic equilibrium flow and a control problem.