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Coupled McKean–Vlasov Equations Over Convex Domains

Author

Listed:
  • Guangying Lv

    (Nanjing University of Information Science and Technology)

  • Wei Wang

    (Nanjing University)

  • Jinlong Wei

    (Zhongnan University of Economics and Law)

Abstract

In this paper, the reflected McKean–Vlasov diffusion ov a convex domain is studied. We first establish the well-posedness of a coupled system of nonlinear stochastic differential equations via a fixed point theorem which is similar to that for partial differential equations. Moreover, the reason why we make different assumptions on drift and cross terms is given. Then, the propagation of chaos for the particle system is also obtained.

Suggested Citation

  • Guangying Lv & Wei Wang & Jinlong Wei, 2024. "Coupled McKean–Vlasov Equations Over Convex Domains," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1824-1849, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-023-01303-3
    DOI: 10.1007/s10959-023-01303-3
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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. Erny, Xavier, 2022. "Well-posedness and propagation of chaos for McKean–Vlasov equations with jumps and locally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 192-214.
    3. Benachour, S. & Roynette, B. & Talay, D. & Vallois, P., 1998. "Nonlinear self-stabilizing processes - I Existence, invariant probability, propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 173-201, July.
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