Hilfer分数阶脉冲随机发展方程的平均原理  

Averaging principle for Hilfer fractional impulsive stochastic evolution equations

作　　者：吕婷 杨敏 王其如[2] LÜTing;YANG Min;WANG Qiru(School of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]太原理工大学数学学院,山西太原030024 [2]中山大学数学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）（中英文）》2024年第1期145-153,共9页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(12001393,12071491);山西省自然科学基金(201901D211103)。

摘　　要：利用分数阶微积分理论、半群性质、不等式技巧和随机分析理论,建立了分数布朗运动驱动的Hilfer分数阶脉冲随机发展方程的平均原理,证明了原方程的适度解均方收敛于无脉冲平均方程的适度解,并通过实例说明了所得理论结果的适用性.By using fractional calculus,semigroup theories,inequality techniques and stochastic analysis theories,an averaging principle for Hilfer fractional impulsive stochastic evolution equations driven by fractional Brownian motion is established.The mild solution of the original equations converges to the mild solution of the reduced averaged equations without impulses in the mean square sense is proved.And an example is presented to illustrate the applicability of our obtained theoretical results.

关 键 词：平均原理 Hilfer分数阶导数 脉冲随机发展方程 分数布朗运动 

分 类 号：O211.63[理学—概率论与数理统计]