Levy过程驱动的随机振动系统逼近  

Approximation of Stochastic Vibration System Driven by Levy Process

作　　者：张梦洁[1] 吕艳 房永磊 ZHANG Mengjie;L Yan;FANG Yonglei(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210000,China;Department of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210000 [2]枣庄学院数学与统计学院,山东枣庄277160

出　　处：《枣庄学院学报》2023年第2期16-20,共5页Journal of Zaozhuang University

基　　金：国家自然科学基金资助项目(11671204)。

摘　　要：研究具有Levy噪声随机振动方程的Smoluchowski-Kramers逼近问题,利用分项估计方法优化随机微分方程模型,证明了在奇异扰动ε趋向于0时,原二阶方程可以由相应的一阶方程进行逼近,原方程的解X_(t)^(ε)依概率收敛到X_(t)^(ε)。In this paper,the Smoluchowski-Kramers approximation problem of the stochastic vibration equation driven by Levy noise is studied,and the stochastic differential equation model is optimized by the itemized estimation method.It is proved that when the singular perturbation tends to 0,the original second-order equation can be approximated by the corresponding first-order equation,and the solution of the original equation X_(t)^(ε) converges in probability to X_(t)^(ε).

关 键 词：随机振动方程 Smoluchowski-Kramers逼近 Levy噪声 

分 类 号：O211.63[理学—概率论与数理统计]