带跳的三角McKean-Vlasov正倒向系统、律依赖单调源与混沌传播
Occupation BAsed Propagation of Chaos for MacKean Vlasov Forward Backward Systems with Jumps and Monotone Sources
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中文总结 AI 辅助
针对带跳的McKean-Vlasov正倒向系统，提出结合混沌传播与占据估计的方法，克服最小选择不连续性，获得改进的收敛速率并验证多个跳模型条件。
中文摘要 AI 辅助
我们研究在非支配概率测度族下带跳的稳健McKean-Vlasov正倒向系统。倒向方程包含一个由非对称损失厌恶驱动的律依赖非光滑单调源。我们建立了系统的适定性与稳定性，分析了其Yosida正则化，并发展了定量粒子近似。主要困难来自最小选择在切换界面上的不连续性，这阻碍了直接Lipschitz估计的使用。为克服这一困难，我们将前向混沌传播与极限前向过程的占据估计相结合。重要的是，粒子系统不需要占据估计。在二阶矩占据条件下，我们获得了粒子与Yosida近似改进的联合收敛速率，控制了前向与倒向状态、鞅被积函数以及累积源。我们还验证了几个具体跳模型的所需占据条件，包括仿射稳定型动力学、可预测变量跳幅以及通过光滑共轭获得的非仿射类。
英文摘要
We study robust Mckean-Vlasov Forxard Backward systems with jumps under a nondominated family of probability measures. The backward equation contains a lawdependent nonsmooth monotone source motivated by asymmetric loss aversion. We establish well-posedness and stability of the system, analyze its Yosida regularization, and develop quantitative particle approximations. The main difficulty comes from the discontinuity of the minimal selection across switching interfaces, which prevents the use of direct Lipschitz estimates. To overcome this difficulty, we combine forward propagation of chaos with occupation estimates for the limiting forward process. Importantly, no occupation estimate is required for the particle system. Under a second-moment occupation condition, we obtain an improved joint convergence rate for the particle and Yosida approximations, controlling the forward and backward states, the martingale integrands, and the accumulated source. We also verify the required occupation conditions for several concrete jump models, including affine stable-like dynamics, predictable variable jump amplitudes, and a non-affine class obtained by smooth conjugacy
