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Keywords = tamed Euler–Maruyama method

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36 pages, 3106 KB  
Article
Tamed Euler–Maruyama Method of Time-Changed McKean–Vlasov Neutral Stochastic Differential Equations with Super-Linear Growth
by Jun Zhang, Liping Xu and Zhi Li
Symmetry 2025, 17(8), 1178; https://doi.org/10.3390/sym17081178 - 23 Jul 2025
Viewed by 558
Abstract
This paper examines temporal symmetry breaking and structural duality in a class of time-changed McKean–Vlasov neutral stochastic differential equations. The system features super-linear drift coefficients satisfying a one-sided local Lipschitz condition and incorporates a fundamental duality: one drift component evolves under a random [...] Read more.
This paper examines temporal symmetry breaking and structural duality in a class of time-changed McKean–Vlasov neutral stochastic differential equations. The system features super-linear drift coefficients satisfying a one-sided local Lipschitz condition and incorporates a fundamental duality: one drift component evolves under a random time change Et, while the other progresses in regular time t. Within the symmetric framework of mean-field interacting particle systems, where particles exhibit permutation invariance, we establish strong convergence of the tamed Euler–Maruyama method over finite time intervals. By replacing the one-sided local condition with a globally symmetric Lipschitz assumption, we derive an explicit convergence rate for the numerical scheme. Two numerical examples validate the theoretical results. Full article
(This article belongs to the Section Mathematics)
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