Stochastic $R_0$ Tensors to Stochastic Tensor Complementarity Problems

The main purpose of this paper is devoted to an introduction of the stochastic tensor complementarity problem. We consider the expected residual minimization formulation of the stochastic tensor complementarity problem. We show that the solution set of the expected residual minimization problem is nonempty and bounded, if the associated tensor is an $R_0$ tensor. We also prove that the associated tensor being a stochastic $R_0$ tensor is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded.