We consider stochastic processes arising from dynamical systems simply by evaluating
an observable function along the orbits of the system and study marked point
processes associated to extremal observations of such time series. In particular, we consider
marked point processes measuring the sum of the excesses over the threshold (AOT)
or measuring the sum of 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, for whose multiplicity distribution we give an explicit formula.
(Joint work with A. C. M. Freitas and J. M. Freitas.)