Occupation BAsed Propagation of Chaos for MacKean Vlasov Forward Backward Systems with Jumps and Monotone Sources
Abstract
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
Related
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- Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay
BibTeX
@misc{tshiswaka2026occupation,
title = {{Occupation BAsed Propagation of Chaos for MacKean Vlasov Forward Backward Systems with Jumps and Monotone Sources}},
author = {Tcheick Kayembe Tshiswaka and Rostin Mabela Matendo and Simon NTumba Badibanga and Jean-Pierre Bosonga Bofeki Lounga},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15346},
eprint = {2609.15346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15346},
}
RIS
TY - UNPB
TI - Occupation BAsed Propagation of Chaos for MacKean Vlasov Forward Backward Systems with Jumps and Monotone Sources
AU - Tcheick Kayembe Tshiswaka
AU - Rostin Mabela Matendo
AU - Simon NTumba Badibanga
AU - Jean-Pierre Bosonga Bofeki Lounga
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.15346
UR - https://arxiv.org/abs/2609.15346
AB - 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
ER -