CHEN, XIAOJUNSHEN, JINGLAI2022-12-222022-12-222022-11-21CHEN, XIAOJUN and JINGLAI SHEN. “Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation,” SIAM J. OPTIM 32 4 (November, 2022): 2909 – 37. https://doi.org/10.1137/21M145536Xhttps://doi.org/10.1137/21M145536Xhttp://hdl.handle.net/11603/26503This paper studies dynamic stochastic variational inequalities (DSVIs) to deal with uncertainties in dynamic variational inequalities (DVIs). We show the existence and uniqueness of a solution for a class of DSVIs in C¹× γ, where C¹ is the space of continuously differentiable functions and γ is the space of measurable functions, and discuss non-Zeno behavior. We use the sample aver-age approximation (SAA) and time-stepping schemes as discrete approximation for the uncertainty and dynamics of the DSVIs. We then show the uniform convergence and an exponential convergence rate of the SAA of the DSVI. A time-stepping EDIIS (energy direct inversion on the iterative subspace) method is proposed to solve the DVI arising from the SAA of DSVI; its convergence is established. Our results are illustrated by a point-queue model for an instantaneous dynamic user equilibrium in traffic assignment problems.29 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Text