摄动Fokker-Planck方程的近似解

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-09-03 DOI:10.1016/j.jmaa.2025.130040

Yan Luo , Kaicheng Sheng

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引用次数: 0

摘要

本文主要研究一类具有时变扰动的Fokker-Planck方程的近似解。构造了该方程近似解的一个公式，并证明了该公式的存在性。相关的哈密顿动力系统解释了这些估计。用Ornstein-Uhlenbeck过程模型和非线性Langevin方程的实例验证了所提结果。我们的工作为福克-普朗克方程和相应的随机微分方程所描述的系统的长期行为提供了更全面的理解。

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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An approximate solution of a perturbed Fokker-Planck equation

This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation is proved. The related Hamiltonian dynamical system explains the estimations. Examples of the Ornstein-Uhlenbeck process model and the nonlinear Langevin equation are used to validate the proposed results. Our work provides a more comprehensive understanding of the long-time behaviour of systems described by this Fokker-Planck equation and the corresponding 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.