The bootstrap and Lyapunov exponents in deterministic chaos. (English) Zbl 0948.37023
The authors discuss “applicability” of the bootstrap to nonlinear stochastic system. Due to the matrix multiplication does not commute, one cannot make specific proposal for bootstrap confidence bounds and as a result the traditional bootstrap cannot be applied when estimating multiplicative ergodic statistics. They suggest a new approach towards quantifying the minimum duration of observation required to estimate global Lyapunov exponents.
Reviewer: Messoud Efendiev (Berlin)
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37H15 | Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents |
| 93B07 | Observability |
| 93E03 | Stochastic systems in control theory (general) |
Software:
bootstrapReferences:
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