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arXiv · 2610.03041

Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With à Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates

Kayembe Tshiswaka Tcheick·Mabela Matendo Rostin·Kabengele Mpunga Yannick·Bosonga Bofeki Jean Pierre
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Abstract

We study a forward-backward McKean-Vlasov system with jumps and one-way coupling: the forward equation is independent of the backward variables, whereas the BSDE depends on the forward state and its law. A source generated by a maximal monotone operator is evaluated along the forward state and then accumulated in the backward equation. The operator is the subdifferential of a convex potential evaluated at the state translated by a function of the control, plus a term depending on the law of the state, so the control shifts the discontinuity interface of its minimal-norm selection. We establish modelwise well-posedness and strong stability, with estimates uniform over the model family. We then study the Yosida approximation: strong convergence, Minty-type strong-weak closedness when the state, its law, and the control (hence the moving interface) vary, and uniform convergence under an integrability condition. For an asymmetric loss-aversion prototype, a quantitative occupation estimate for a layer around the interface yields an explicit Yosida convergence rate. When the continuous martingale part is nondegenerate and the interface moves absolutely continuously, the occupation time is linear in the layer width. The same rate controls the backward components and the cumulative source.

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Kayembe Tshiswaka Tcheick, Mabela Matendo Rostin, Kabengele Mpunga Yannick, Bosonga Bofeki Jean Pierre. 2026-10-02. Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With à Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates. https://arxiv.org/abs/2610.03041

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