Mathematics – Dynamical Systems
Scientific paper
2011-03-04
Mathematics
Dynamical Systems
34 pages, 7 figures; Journal of Statistical Physics 2011
Scientific paper
10.1007/s10955-011-0234-7
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.
Faranda Davide
Lucarini Valerio
Turchetti Giorgio
Vaienti Sandro
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