LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS-Reference-Cited by-同舟云学术

LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

Published:2001-03 Issue:01 Volume:01 Page:127-157
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

CONG NGUYEN DINH¹

Affiliation:

1. Hanoi Institute of Mathematics, P. O. Box 631 Bo Ho, 10000 Hanoi, Vietnam

Abstract

We introduce a concept of Lyapunov exponents and Lyapunov spectrum for nonautonomous linear stochastic differential equations. The Lyapunov exponents are defined samplewise via the two-parameter flow generated by the equation. We prove that Lyapunov exponents are finite and nonrandom. Lyapunov exponents are used for investigation of Lyapunov regularity and stability of nonautonomous stochastic differential equations. The results show that the concept of Lyapunov exponents is still very fruitful for stochastic objects and gives us a useful tool for investigating sample stability as well as qualitative behavior of nonautonomous linear and nonlinear stochastic differential equations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493701000084

Reference7 articles.

1. Perfect cocycles through stochastic differential equations

2. A property of systems of differential equations perturbed by white noises and its applications to the stochastic continuity of lyapunov exponents

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