One-Dimensional McKean-Vlasov Stochastic Variational Inequalities and Coupled BSDEs with Locally Holder Noise Coefficients

TL;DR

This paper establishes the existence and uniqueness of solutions for three classes of McKean-Vlasov stochastic equations with locally Holder continuous coefficients, including variational inequalities and coupled forward-backward systems.

Contribution

It introduces new methods to prove well-posedness for these equations with locally Holder continuous coefficients, covering a broad class of stochastic systems.

Findings

Proved well-posedness for McKean-Vlasov SDEs with variational inequalities.

Extended results to coupled forward-backward systems with locally Holder coefficients.

Developed strategies for handling stochastic coefficients with limited regularity.

Abstract

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.