Small perturbations may change the sign of Lyapunov exponents for linear SDEs

被引：2

作者：

Cheng, Xianjin ^{[1
]}

Liu, Zhenxin ^{[2
,3
]}

Zhang, Lixin ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math, Dalian 116024, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[3] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2023年

关键词：

Lyapunov exponent; linear stochastic differential equation; exponentially decaying perturbation; POSITIVE CHARACTERISTIC EXPONENTS;

D O I：

10.1142/S021949372240038X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study the existence of n-dimensional linear stochastic differential equations (SDEs) such that the sign of Lyapunov exponents is changed under an exponentially decaying perturbation. First, we show that the equation with all positive Lyapunov exponents will have n - 1 linearly independent solutions with negative Lyapunov exponents under the perturbation. Meanwhile, we prove that the equation with all negative Lyapunov exponents will also have solutions with positive Lyapunov exponents under another similar perturbation. Finally, we show that other three kinds of perturbations which appear at different positions of the equation will change the sign of Lyapunov exponents.

引用

页数：25

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