奇異攝動的擴散系統弱收斂意義下的平均化原理：直接平均法的概述與進展

摘 要：主要介紹了建立奇異攝動的擴散系統的隨機平均化原理的直接平均方法和當前的進展，這種方法主要基于鞅問題和弱收斂.最后一部分也介紹了這種方法當前在奇異攝動的延遲和泛函系統的隨機平均化原理中的進展和困難.

關鍵詞：奇異攝動；擴散系統；隨機平均化原理；鞅問題；弱收斂

中圖分類號：O211文獻標志碼：A

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The averaged principle of diffusion systems with singular perturbations in the sense of weak convergence： overview and advancement of the direct-averaging method

Wu Fuke

（School of Mathematics and Statistics， Huazhong University of Science and Technology， Wuhan 430074， China）

Abstract： This paper mainly introduces the direct-averaging method for stochastic averaged principle of diffusion systems with singular perturbations， which is based on the martingale problem and the weak convergence. Finally， the advances and difficulties of this method in stochastic averaged principle of the diffusion delay and functional diffusion systems with singular perturbations.

Keywords： singular perturbation; diffusion system; stochastic averaged principle; martingale problem; weak convergence

［責任編校 陳留院 趙曉華］

收稿日期：2023-02-09;修回日期：2023-02-15.

基金項目：國家自然科學基金（62273158）.

作者簡介（通信作者）：

吳付科（1976-），男，河南鄧州人，華中科技大學教授，博士，國家優青，研究方向為隨機微分方程及其應用，E-mail：wufuke@hust.edu.cn.