Stability of exact and numerical solutions for McKean–Vlasov stochastic differential equations with Hölder diffusion coefficients

Zhuoqi Liu, Shuaibin Gao and Qian Guo

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 746-760

Abstract: This paper investigates the long-time behavior of highly nonlinear McKean–Vlasov stochastic differential equations (MVSDEs) with Hölder continuous diffusion coefficients and their numerical approximations, which play an important role in the analysis of some real-world models. Based on the Yamada–Watanabe approximation technique, the primary goal is to prove that the exact solution tends to the equilibrium state in pth moment sense with p>0. Then, the propagation of chaos between the interacting particle system and non-interacting one is derived in the infinite horizon. To approximate such equations, a modified tamed Euler–Maruyama scheme is constructed for the corresponding interacting particle system, and its mean-square stability is rigorously demonstrated. We reveal that the numerical solution can reproduce the stability of the underlying MVSDE. The final part presents the numerical examples of long-time propagation of chaos and the mean-square stability of numerical solution, which are consistent with the theoretical results.

Keywords: McKean–Vlasov stochastic differential equations; Stability; Hölder diffusion coefficients; Yamada–Watanabe approximation technique; Modified tamed Euler–Maruyama scheme (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:746-760

DOI: 10.1016/j.matcom.2026.02.031

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