Title: Rare events point processes for chaotic dynamical systems
Authors: Ana Freitas - Universidade do Porto (Portugal) [presenting]
Abstract: Stochastic processes are considered arising from dynamical systems by evaluating an observable function (which achieves a global maximum at a single point of the phase space) along the orbits of the system. We associate the existence of an Extremal Index less than 1 to the occurrence of a periodic phenomena. We show that, under certain conditions, in the absence of clustering, the point processes of exceedances converge to a standard Poisson process. In the presence of clustering, the point processes converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances with a geometric distribution ruling its multiplicity.