Moment Lyapunov exponents are important characteristic numbers for describing the dynamic stability of a stochastic system. When the moment Lyapunov exponent is negative, the moment of the solution of the stochastic system is stable. Monte Carlo simulation approaches complement approximate analytical methods in the determination of moment Lyapunov exponents and provides criteria on assessing the accuracy of approximate analytical results. For stochastic dynamical systems described by Itô stochastic differential equations, the solutions are diffusion processes and their variances may increase with time. Due to the large variances of the solutions and round-off errors, bias errors in the simulation of moment Lyapunov exponents are significant in improper numerical algorithms. An improved algorithm for simulating the moment Lyapunov exponents of linear homogeneous stochastic systems is presented in this paper.
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May 2009
Research Papers
Simulation of Moment Lyapunov Exponents for Linear Homogeneous Stochastic Systems
Wei-Chau Xie,
Wei-Chau Xie
Department of Civil and Environmental Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
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Qinghua Huang
Qinghua Huang
Department of Civil and Environmental Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
Search for other works by this author on:
Wei-Chau Xie
Department of Civil and Environmental Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
Qinghua Huang
Department of Civil and Environmental Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, CanadaJ. Appl. Mech. May 2009, 76(3): 031001 (10 pages)
Published Online: March 3, 2009
Article history
Received:
March 14, 2006
Revised:
October 2, 2008
Published:
March 3, 2009
Citation
Xie, W., and Huang, Q. (March 3, 2009). "Simulation of Moment Lyapunov Exponents for Linear Homogeneous Stochastic Systems." ASME. J. Appl. Mech. May 2009; 76(3): 031001. https://doi.org/10.1115/1.3063629
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