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Coupling by change of measure for conditional McKean–Vlasov SDEs and applications

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  • Huang, Xing

Abstract

The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean–Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy for mean field interacting particle system with common noise. For the log-Harnack inequality, two different types of couplings will be constructed for non-degenerate conditional McKean–Vlasov SDEs with multiplicative noise. As to the quantitative conditional propagation of chaos in relative entropy, the initial distribution of interacting particle system is allowed to be singular with that of limit equation. The above results are also extended to conditional distribution dependent stochastic Hamiltonian system.

Suggested Citation

  • Huang, Xing, 2025. "Coupling by change of measure for conditional McKean–Vlasov SDEs and applications," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002163
    DOI: 10.1016/j.spa.2024.104508
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    1. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    2. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    3. Lijun Bo & Tongqing Li & Xiang Yu, 2021. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Papers 2106.09978, arXiv.org, revised May 2022.
    4. Bo, Lijun & Li, Tongqing & Yu, Xiang, 2022. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 622-654.
    5. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
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