Well-posedness of stochastic variational inequalities with discontinuous drifts

In this paper, we investigate the well-posedness of stochastic variational inequalities on [Formula: see text] with discontinuous drift coefficients. First, a case that drift coefficients are only integrable on [Formula: see text] is considered. Utilizing Girsanov’s theorem, Zvonkin’s transform and Yamada–Watanabe’s principle, we derive the weak well-posedness if [Formula: see text] and strong well-posedness if [Formula: see text]. Second, if the drift coefficients are piecewise Lipschitz continuous and [Formula: see text], strong well-posedness is also obtained by virtue of a transform which regularizes the discontinuous drifts.