Abstract
The moment Lyapunov exponents are important characteristic numbers for determining the dynamical stability of stochastic systems. Monte Carlo simulations are complement to the approximate analytical methods in the determination of the moment Lyapunov exponents. They also provide criteria on assessing how accurate the approximate analytical methods are. For stochastic dynamical systems described by Itô stochastic differential equations, the solutions are diffusion processes and their variances may increase with time of simulation. Due to the large variances of the solutions and round-off errors, bias errors in the simulation of momemt Lyapunov exponents are significant in the cases of improper numerical approaches. The improved estimation for some systems is presented in this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Arnold. Stochastic Differential Equations: Theory and Applications. John Wiley & Sons, Inc., New York, 1974.
W. Feller. An Introduction to Probability Theory and Its Applications, volume 2. John Wiley & Sons, Inc., New York, second edition, 1965.
B.V. Gnedenko and A.N. Kolmogorov. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley Publishing Company, Inc., 1954. Translated from the Russian.
R.Z. Khasminskii. A limit theorem for the solutios of differential equations with random right-hand sides. Theory of Probability and Its Applications, 11(3):390–406, 1966a. English translation.
R.Z. Khasminskii. On stochastic processes de_ned by differential equations with a small parameter. Theory of Probability and Its Applications, 11(2):211–228, 1966b. English translation.
R.Z. Khasminskii. Stochastic Stability of Differential Equations. Kluwer Academic Publishers, Norwell, MA, 1980. English translation.
G.S. Larinov. Investigation of the vibration of relaxing systems by the averaging method. Mechanics of Polymers, 5:714–720, 1969. English translation.
W.C. Xie. Monte carlo simulation of moment Lyapunov exponents. Journal of Applied Mechanics, 72 (2):269–275, 2005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Xie, WC., Huang, Q. (2006). On the Monte Carlo Simulation of Moment Lyapunov Exponents. In: Pandey, M., Xie, WC., Xu, L. (eds) Advances in Engineering Structures, Mechanics & Construction. Solid Mechanics and Its Applications, vol 140. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4891-2_53
Download citation
DOI: https://doi.org/10.1007/1-4020-4891-2_53
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4890-6
Online ISBN: 978-1-4020-4891-3
eBook Packages: EngineeringEngineering (R0)