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Mean-field forward–backward stochastic differential equations driven by G-Brownian motion

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  • Sun, Shengqiu

Abstract

In this paper, we consider the mean-field forward–backward stochastic differential equations driven by G-Brownian motion with Lipschitz coefficients. The existence and uniqueness of solution on small time duration can be obtained by contraction mapping principle and some a prior estimates.

Suggested Citation

  • Sun, Shengqiu, 2025. "Mean-field forward–backward stochastic differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000744
    DOI: 10.1016/j.spl.2025.110429
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    References listed on IDEAS

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    1. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    2. Li, Hanwu & Peng, Shige, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
    3. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
    6. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    7. Hui Min & Ying Peng & Yongli Qin, 2014. "Fully Coupled Mean‐Field Forward‐Backward Stochastic Differential Equations and Stochastic Maximum Principle," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Bensoussan, A. & Yam, S.C.P. & Zhang, Z., 2015. "Well-posedness of mean-field type forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3327-3354.
    9. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    10. Hui Min & Ying Peng & Yongli Qin, 2014. "Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, April.
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