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One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients

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  • Ning, Ning
  • Wu, Jing
  • Zheng, Jinwei

Abstract

In this article, we investigate three classes of equations: the McKean–Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean–Vlasov stochastic variational inequality (MVSVI), and the coupled forward–backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Hölder continuity and employ different strategies to achieve that for each class.

Suggested Citation

  • Ning, Ning & Wu, Jing & Zheng, Jinwei, 2024. "One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:spapps:v:171:y:2024:i:c:s0304414924000218
    DOI: 10.1016/j.spa.2024.104315
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    References listed on IDEAS

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    1. Adams, Daniel & dos Reis, Gonçalo & Ravaille, Romain & Salkeld, William & Tugaut, Julian, 2022. "Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 264-310.
    2. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    3. Ren, Panpan, 2023. "Singular McKean–Vlasov SDEs: Well-posedness, regularities and Wang’s Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 291-311.
    4. Jin Ma & Jakša Cvitanić, 2001. "Reflected forward-backward SDE s and obstacle problems with boundary conditions," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-26, January.
    5. Wang, Feng-Yu, 2023. "Exponential ergodicity for singular reflecting McKean–Vlasov SDEs," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 265-293.
    6. Chaudru de Raynal, P.E., 2020. "Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 79-107.
    7. Huang, Xing & Wang, Feng-Yu, 2019. "Distribution dependent SDEs with singular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4747-4770.
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