由时变Lévy噪声驱动的随机微分方程的平均值原理

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 492-500.

由时变Lévy噪声驱动的随机微分方程的平均值原理

程丽娟¹(),任永^1,^2,*(),王露²()

¹ 岭南师范学院数学与统计学院广东湛江 524048
² 安徽师范大学数学系安徽芜湖 241000

收稿日期:2018-11-13 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 任永 E-mail:chenglijuan666@126.com;renyong@126.com;wanglu03057465@126.com
作者简介:程丽娟, E-mail:chenglijuan666@126.com|王露, E-mail:wanglu03057465@126.com
基金资助:
国家自然科学基金(11871076)

Averaging Principles for Stochastic Differential Equations Driven by Time-Changed Lévy Noise

Lijuan Cheng¹(),Yong Ren^1,^2,*(),Lu Wang²()

¹ School of Mathematics and Statistics, Lingnan Normal University, Guangdong Zhanjiang 524048
² Department of Mathematics, Anhui Normal University, Anhui Wuhu 241000

Received:2018-11-13 Online:2020-04-26 Published:2020-05-21
Contact: Yong Ren E-mail:chenglijuan666@126.com;renyong@126.com;wanglu03057465@126.com
Supported by:
the NSFC(11871076)

摘要/Abstract

摘要：

该文讨论了一类由时变Lévy噪声驱动的随机微分方程（LSDE）的平均值原理，提出了其均值化方程，在均方和以概率意义下得到了均值化方程的解收敛到原LSDE的解，给出了一个具体例子.

关键词: 平均值原理, 随机微分方程, 时变Lévy噪声

Abstract:

This paper concerns averaging principles for a kind of stochastic differential equations driven by time-changed Lévy noise (LSDEs, in short). An averaged LSDE for the original LSDE is proposed. The solution of the averaged LSDE converges to that of the original LSDE in the sense of mean square and probability. Finally, we will give an example to illustrate the obtained results.

Key words: Averaging principle, Stochastic differential equation, Time-changed Lévy noise

中图分类号:

O211

程丽娟,任永,王露. 由时变Lévy噪声驱动的随机微分方程的平均值原理[J]. 数学物理学报, 2020, 40(2): 492-500.

Lijuan Cheng,Yong Ren,Lu Wang. Averaging Principles for Stochastic Differential Equations Driven by Time-Changed Lévy Noise[J]. Acta mathematica scientia,Series A, 2020, 40(2): 492-500.

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