g -布朗运动驱动下分布相关SDEs的稳定性和平均原理

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-08-29 DOI:10.1016/j.jmaa.2025.130024

Wensheng Yin , Yong Ren , Kaile Cao

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引用次数: 0

摘要

研究了由g -布朗运动驱动的分布相关随机微分方程的渐近性质。在Lipschitz条件下，研究了指数二阶矩极限有界性、稳定性和平均原理。在非lipschitz条件下，我们首先采用carathacimodory逼近方法证明了分布相关G-SDEs的存在唯一性。特别地，我们处理了快速时间振荡分布相关的G-SDEs，它的解可以用平均条件下的平均分布相关的G-SDEs来逼近。此外，还提供了两个说明性示例来验证平均分布相关的G-SDEs。

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Stability and averaging principle for distribution dependent SDEs driven by G-Brownian motion

This paper concerns the asymptotic behavior for distribution dependent stochastic differential equations driven by G-Brownian motion (G-SDEs). Under Lipschitz condition, we study exponentially second-moment ultimate boundedness, stability and averaging principle. Under non-Lipschitz condition, we first prove the existence and uniqueness for distribution dependent G-SDEs by adopting Carathéodory approximation approach. In particular, the fast time oscillating distribution dependent G-SDEs is treated and its solution can be approximated by the averaged distribution dependent G-SDEs under averaging condition. Additionally, two illustrative examples are provided to validate the averaged-distribution-dependent G-SDEs.

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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.