α-稳定噪声驱动随机微分方程强平均化原理  

Strong averaging principle for multiscale SDEs driven byα-stable process

作　　者：魏华 周跃进 WEI Hua;ZHOU Yuejin(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报(自然科学版)》2025年第2期219-225,共7页Journal of Harbin University of Commerce:Natural Sciences Edition

基　　金：深部煤矿采动响应与灾害防控国家重点实验室基金资助项目(SKLMRDPC22KF03)。

摘　　要：探究了可乘α-稳定噪声驱动且系数仅仅满足Holder连续性,快、慢随机动力系统关于强收敛的渐近性.采用关于非局部Poisson方程的最优正则估计技术,拟建立关于强收敛的平均化原理,强平均化原理也被称为泛函版本的大数定律.前期的研究主要集中在Brown运动噪声或者可加Lévy噪声驱动的随机动力系统强、弱平均化原理,现存的文献中关于可乘Lévy噪声驱动快、慢随机动力系统关于强、弱收敛渐近行为的研究还很少,关于可乘Lévy噪声的情形需要克服本质困难,本文的结果是全新的.此外,还得到了关于强收敛的最优收敛速度.This paper explored the asymptotic behavior of fast and slow stochastic dynamical systems with strong convergence driven by multiplicativeα-stable noise and coefficients that only satisfy Holder continuity,using the optimal regularization estimation technique for non local Poisson equations,established an averaging principle for strong convergence,also known as the functional version of the law of large numbers Previous research has mainly focused on the strong and weak averaging principles of stochastic dynamical systems driven by Brown motion noise or additive Lévy noise.There was still little existing literature on the strong and weak convergence asymptotic behavior of fast and slow stochastic dynamical systems driven by multiplicative Lévy noise.Regarding the case of multiplicative Lévy noise,need to overcome essential difficulties.The results of this paper were novel.In addition,the optimal convergence speed for strong convergence also was obtained.

关 键 词：非局部Poisson方程 强平均化原理 α-稳定过程 LÉVY过程 强收敛 

分 类 号：O211[理学—概率论与数理统计]