分数布朗运动和标准布朗运动驱动的一类与分布相关的慢速随机微分方程的平均原理

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI:10.1016/j.jmaa.2025.129628

Shitao Liu

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引用次数: 0

摘要

研究了一类由多维标准布朗运动和具有Hurst参数1/2<；H<；1的多维分数布朗运动同时驱动的与分布相关的慢速随机微分方程。利用Picard迭代证明了系统的存在唯一性。此外，研究了强平均原理，表明系统的慢变量可以通过求解相关的平均随机微分方程来有效地逼近。

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Averaging principle for a class of distribution dependent slow-fast stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

This paper investigates a class of distribution dependent slow-fast stochastic differential equations driven simultaneously by multidimensional standard Brownian motions and a multidimensional fractional Brownian motion with Hurst parameter

1 / 2 < H < 1

. Existence and uniqueness of the system is proved by using the Picard iteration. Moreover, strong averaging principle is studied to show that slow variable of the system can be efficiently approximated by solution of associated averaged stochastic differential equation.

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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.