关于具有非全局 Lipschitz 连续和超线性增长漂移与扩散系数的 Lévy 驱动型 McKean-Vlasov SDEs 的无限时间跨度近似问题

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-22 DOI:10.1016/j.jmaa.2024.128982

Ngoc Khue Tran , Trung-Thuy Kieu , Duc-Trong Luong , Hoang-Long Ngo

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引用次数: 0

摘要

本文研究了由勒维过程驱动的麦金-弗拉索夫随机微分方程的数值近似。我们提出了一种驯服自适应的 Euler-Maruyama 方案，并考虑了它在有限和无限时间范围内的强收敛性，该方案适用于一些具有非全局 Lipschitz 连续和超线性增长漂移和扩散系数的 Lévy 驱动的 McKean-Vlasov 随机微分方程。

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On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

This paper studies the numerical approximation for McKean-Vlasov stochastic differential equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite time horizons when applying for some classes of Lévy-driven McKean-Vlasov stochastic differential equations with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.