An averaging principle for stochastic dynamical systems with Levy noise

被引：164
作者：
Xu, Yong [1 ]
Duan, Jinqiao [2 ]
Xu, Wei [1 ]
机构：
[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Peoples R China
[2] IIT, Dept Appl Math, Chicago, IL 60616 USA
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2011年 / 240卷 / 17期
基金：
美国国家科学基金会;
关键词：
Averaging principle; Stochastic differential equations; Non-Gaussian Levy noise; Convergence to the averaged system;
D O I：
10.1016/j.physd.2011.06.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to establish an averaging principle for stochastic differential equations with non-Gaussian Levy noise. The solutions to stochastic systems with Levy noise can be approximated by solutions to averaged stochastic differential equations in the sense of both convergence in mean square and convergence in probability. The convergence order is also estimated in terms of noise intensity. Two examples are presented to demonstrate the applications of the averaging principle, and a numerical simulation is carried out to establish the good agreement. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：1395 / 1401
页数：7
相关论文
共 32 条
[1]  
[Anonymous], 2009, Levy processes and stochastic calculus
[2]  
Bertoin J., 1998, CAMBRIDGE TRACTS MAT, V121
[3]  
Bogoliubov N.N., 1961, Asymptotic Methods in the Theory of Non-linear Oscillations
[4]  
Freidlin MI, 2012, Random Perturbations of Dynamical Systems
[5]  
Gihman I.I., 1972, STOCHASTIC DIFFERENT
[6]  
Khas'minskii R. Z., 1968, Kybernetika, V4, P260
[7]   A LIMIT THEOREM FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH RANDOM RIGHT-HAND SIDES [J].
KHASMINSKII, RZ .
THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (03) :390-+
[8]  
KHASMINSKII RZ, 1963, THEORY PROBAB APPL, V8
[9]  
Klebaner F.C., 2005, Introduction to Stochastic Calculus with Applications, V2
[10]  
KOLOMIETS VG, 1991, UKR MATH J, V43, P242
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