分数阶布朗运动驱动非线性延迟中立型McKean-Vlasov SDEs的收敛速率

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-04-26 DOI:10.1016/j.amc.2025.129478

Shengrong Wang , Jie Xie , Li Tan

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引用次数: 0

摘要

本文的主要目的是研究一类具有超线性延迟的中立型McKean-Vlasov随机微分方程的强收敛性，该方程由分数阶布朗运动驱动，且Hurst指数H∈(1/2,1)。在给出精确解的唯一性和存在性之后，分析了混沌的矩有界性和混沌的传播性。此外，给出了Euler-Maruyama （EM）格式，并证明了数值解强收敛于真解。最后，给出了一个相关的实例来说明该理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions

The primary objective of this paper is to explore the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent

H \in (1 / 2, 1)

. After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama (EM) scheme and show that the numerical solution convergent to the true solution strongly. Furthermore, a related example is given to illustrate the theory.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.