双尺度随机时滞微分方程的平均原理
The Averaging Principle of Two-Scale Stochastic Delay Differential Equation
摘要: 本文研究了分数布朗运动驱动的非自治双尺度随机时滞微分方程的平均原理。首先，通过广义Stieltjes积分和随机平均原理，推导了非自治双尺度系统的均方收敛定理。然后，结合均方收敛定理和停时理论，分别得到了原系统和平均系统的矩估计。最后，证明了当时间尺度参数趋于零时，慢变量方程的解过程在均方意义下收敛于平均方程的解过程。
Abstract: The main goal of this article is to study an average principle of a class of non-autonomous two time-scale stochastic differential delay equations driven by fractional Brownian motion. Firstly, the mean square convergence theorem for non-autonomous scale systems was derived by means of Generalized Stieltjes integral and Stochastic Average Principle. Then, combining the mean square convergence theorem and the Stopping-time theory, the moment estimates of the original system and the average system were obtained, respectively. Finally, it showed that when the time scale pa-rameters approach zero, the solution process of the slow variable equation converges to the solution process of the mean equation in the mean square sense.
文章引用：贺鑫. 双尺度随机时滞微分方程的平均原理[J]. 应用数学进展, 2024, 13(2): 788-805. https://doi.org/10.12677/AAM.2024.132077

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