Well-posedness of stochastic variational inequalities with discontinuous drifts.

In this paper, we investigate the well-posedness of stochastic variational inequalities on ℝ d with discontinuous drift coefficients. First, a case that drift coefficients are only integrable on (0 , T) × ℝ d is considered. Utilizing Girsanov's theorem, Zvonkin's transform and Yamada–Watanabe's principle, we derive the weak well-posedness if d > 1 and strong well-posedness if d = 1. Second, if the drift coefficients are piecewise Lipschitz continuous and d = 1 , strong well-posedness is also obtained by virtue of a transform which regularizes the discontinuous drifts. [ABSTRACT FROM AUTHOR]