On the approximation of monotone variational inequalities in L^p spaces with probability measure

n this paper we propose an approximation procedure for a class of monotone variational inequalities in probabilistic Lebesgue spaces. The implementation of the functional approximation in Lp, with p > 2, leads to a finite dimensional variational inequality whose structure is different from the one obtained in the case p = 2, already treated in the literature. The proposed computational scheme is applied to the random traffic equilibrium problem with polynomial cost functions.