2023/07/18 by Ning Ning, Jing Wu, Ning, Ning +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2307.09678
openalex publication_date 2023/07/18 · openalex created_date 2023/07/21 · openalex updated_date 2026/07/28
In this article, we investigate three classes of equations: the McKean-Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean-Vlasov stochastic variational inequality (MVSVI), and the coupled forward-backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Holder continuity and employ different strategies to achieve that for each class.