Levitin–Polyak well-posedness of stochastic variational inequalities and applications to a random spatial price equilibrium problem

The aim of the paper is to study the Levitin–Polyak well-posedness (shortly, LP well-posedness) of stochastic variational inequalities. A characterization of the LP well-posedness is obtained considering the size of LP approximating solution sets. The equivalence between the LP well-posedness of a stochastic variational inequality with the existence and uniqueness of  its solution is proved. In addition, the LP well-posedness in the generalized sense is characterized. Finally, the theoretical results are applied to the random spatial price equilibrium problem in the price formulation.