B0647
Title: Area and peaks over thresholds processes dynamically generated
Authors: Jorge Freitas - Universidade do Porto (Portugal) [presenting]
Abstract: Stochastic processes arising from dynamical systems are considered by evaluating an observable function along the orbits of the system. We study marked point processes associated to extremal observations of such time series corresponding to exceedances of high thresholds. Each exceedance is marked by a quantity intended to measure the severity of the exceedance or simply to count them. In particular, we consider marked point processes measuring the aggregate damage by adding all the excesses over the threshold that mark each exceedance (AOT) or simply by adding the largest excesses in a cluster of exceedances (POT). We provide conditions to prove the convergence of such marked point processes to a compound Poisson process, with particular multiplicity distributions.
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