Explicit formulas for the top Lyapunov exponents of planar linear stochastic differential equations

被引：0

作者：

Pham The Anh ^{[1
]}

Doan Thai Son ^{[2
]}

机构：

[1] Le Quy Don Tech Univ, Dept Math, Hanoi, Vietnam

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2017年 / 35卷 / 04期

关键词：

Multiplicative ergodic theorem; Lyapunov exponent; stochastic differential equation; stability; stochastic bifurcation; SYSTEMS; STABILITY;

D O I：

10.1080/07362994.2017.1305908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this article is to establish explicit formulas for the top Lyapunov exponents of planar linear stochastic differential equations. We use these formulas to examine the sample-path stability of a linear stochastic differential equations arising in fluid dynamics and of a model of stochastic Hopf bifurcation.

引用

页码：662 / 676

页数：15

共 50 条

[41] Stochastic Lyapunov Stability for Rough Differential Equations
Nishimura, Yuki
2019 18TH EUROPEAN CONTROL CONFERENCE (ECC), 2019, : 1164 - 1169
[42] APPROXIMATION OF UPPER LYAPUNOV EXPONENTS OF BILINEAR STOCHASTIC DIFFERENTIAL-SYSTEMS
TALAY, D
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (04) : 1141 - 1164
[43] LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX-1
Nguyen Dinh Cong
Nguyen Thi The
STOCHASTICS AND DYNAMICS, 2012, 12 (04)
[44] APPROXIMATION OF LYAPUNOV EXPONENTS OF STOCHASTIC DIFFERENTIAL-SYSTEMS ON COMPACT MANIFOLDS
GRORUD, A
TALAY, D
LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 1990, 144 : 704 - 713
[45] A PROPERTY OF SYSTEMS OF DIFFERENTIAL-EQUATIONS PERTURBED BY WHITE NOISES AND ITS APPLICATIONS TO THE STOCHASTIC CONTINUITY OF LYAPUNOV EXPONENTS
CONG, ND
STOCHASTIC ANALYSIS AND APPLICATIONS, 1993, 11 (04) : 423 - 439
[46] Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equations
Ford, Neville J.
Norton, Stewart J.
ALGORITHMS FOR APPROXIMATION, PROCEEDINGS, 2007, : 309 - +
[47] Adjoint equation and Lyapunov regularity for linear stochastic differential algebraic equations of index 1
Nguyen Dinh Cong
Siegmund, Stefan
Nguyen Thi The
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2014, 86 (05) : 776 - 802
[48] EXPLICIT FORMULAS FOR COMPLETIONS OF LINEAR-TIME VARYING SINGULAR SYSTEMS OF DIFFERENTIAL-EQUATIONS
CAMPBELL, SL
RAKOWSKI, M
CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 1994, 13 (2-3) : 185 - 199
[49] Explicit solutions for multivalued stochastic differential equations
Xu, Siyan
STATISTICS & PROBABILITY LETTERS, 2008, 78 (15) : 2281 - 2292
[50] Explicit Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
NUMERICAL ANALYSIS OF MULTISCALE COMPUTATIONS, 2012, 82 : 1 - 22

← 1 2 3 4 5 →