Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With à Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates
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.
Related
- Occupation BAsed Propagation of Chaos for MacKean Vlasov Forward Backward Systems with Jumps and Monotone Sources
- Well-posedness, regularity and stability for linear Maxwell's equations with interface damping
- Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion
- A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition
- Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay
BibTeX
@misc{tcheick2026forwardbackward,
title = {{Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With à Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates}},
author = {Kayembe Tshiswaka Tcheick and Mabela Matendo Rostin and Kabengele Mpunga Yannick and Bosonga Bofeki Jean Pierre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03041},
eprint = {2610.03041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03041},
}
RIS
TY - UNPB
TI - Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With à Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates
AU - Kayembe Tshiswaka Tcheick
AU - Mabela Matendo Rostin
AU - Kabengele Mpunga Yannick
AU - Bosonga Bofeki Jean Pierre
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03041
UR - https://arxiv.org/abs/2610.03041
AB - 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.
ER -