Multi-dimensional Path-dependent Forward-backward Stochastic Variational Inequalities

In this article, we consider a system of stochastic variational inequalities (SVIs) in the differential form. The system has a d -dimensional forward SVI X that depends on its path and carries a subdifferential operator, and a n -dimensional backward SVI coupled with X through the path of X and has another subdifferential operator. This system extends all classical stochastic processes to SVIs with general path-dependence, and enables classical SVIs with random coefficient functions. Through delicate infinite-dimensional analyses and forward-backward stochastic analyses, we establish its well-posedness of a unique strong solution under mild regularity conditions.