发表机构
University of Kinshasa（金沙萨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带跳跃和单向耦合的向前-向后McKean-Vlasov系统，其中极大单调源沿状态求值且界面受控制平移；建立了适定性、稳定性，并给出Yosida近似的显式收敛速率。
AI 中文摘要
我们研究了一个带跳跃和单向耦合的向前-向后McKean-Vlasov系统：向前方程独立于向后变量，而BSDE依赖于向前状态及其分布。由极大单调算子生成的源沿向前状态求值，然后累积到向后方程中。该算子是凸势函数在状态（由控制函数平移）处的次微分，加上一个依赖于状态分布的项，因此控制平移了其最小范数选择的间断界面。我们建立了模型族的适定性和强稳定性，并给出了对模型族一致的估计。随后我们研究了Yosida近似：强收敛性，当状态、其分布和控制（从而移动界面）变化时的Minty型强-弱闭性，以及在可积性条件下的均匀收敛性。对于一个非对称损失厌恶原型，界面周围层的定量占据估计给出了显式的Yosida收敛速率。当连续鞅部分非退化且界面绝对连续移动时，占据时间与层宽成线性关系。相同的速率控制着向后分量和累积源。
英文摘要
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.
