Regularization of stochastic variational inequalities and a comparison of an LpLp and a sample-path approach

This paper aims to study stochastic variational inequalities with special emphasis to incorporate uncertainty in transportation models. The main contribution of this paper is two fold. First, we introduce the so-called elliptic regularization technique in the context of stochastic variational inequalities. Our motivation to study regularization is due to the fact that network problems lead naturally to monotone variational inequalities. Therefore, to employ computational methods which are designed for strongly monotone variational inequalities, we resort to the regularization. Second, we perform a thorough comparison of our approach which is a rigorous LpLp approach, with a commonly studied sample-path approach for stochastic variational inequalities. Two small scale network equilibrium problems are analyzed in detail to better illustrate the conceptual difference between the two approaches as well as the commonly used computational methods.