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arXiv · 2307.09678

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

Ning Ning·Jing Wu·Jinwei Zheng
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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.

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Ning Ning, Jing Wu, Jinwei Zheng. 2024-01-30. One-Dimensional McKean-Vlasov Stochastic Variational Inequalities and Coupled BSDEs with Locally Holder Noise Coefficients. https://arxiv.org/abs/2307.09678

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