Abstract
In this paper we review some results about the approximation of the upper Lyapunov exponents λ of linear and nonlinear diffusion processes X. The stochastic differential system solved by X is discretized by the Euler scheme. Under appropriate assumptions, the upper Lyapunov exponent \( \bar \lambda \) of the resulting approximate process \( \bar X \) is well defined and can be efficiently computed by simulating one single trajectory of \( \bar X \) during a time long enough. We describe the mathematical technique which leads to estimates on the convergence rate of \( \bar \lambda \) to λ. We start by an elementary example, then we deal with linear systems, and finally we consider nonlinear systems.
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Talay, D. (1999). The Lyapunov Exponent of the Euler Scheme for Stochastic Differential Equations. In: Stochastic Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-22655-9_10
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DOI: https://doi.org/10.1007/0-387-22655-9_10
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