Coupled McKean–Vlasov Equations Over Convex Domains

Guangying Lv (), Wei Wang () and Jinlong Wei ()
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Guangying Lv: Nanjing University of Information Science and Technology
Wei Wang: Nanjing University
Jinlong Wei: Zhongnan University of Economics and Law

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1824-1849

Abstract: 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.

Keywords: Propagation of chaos; McKean–Vlasov equations; Particle system; Reflection diffusions; 60H10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01303-3

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