On the Monte Carlo simulation of moment Lyapunov exponents

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. © 2006 Springer.