  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
corresponding to exceedances of high thresholds. Each exceedance is marked by a
quantity intended to measure the severity of the exceedance. 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, for whose multiplicity distribution we give an
explicit formula. These conditions are shown to follow from a strong form of
decay of correlations of the system. Moreover, we prove that the convergence of
the marked point processes for a `nice' first return induced map can be carried
to the original system. The systems considered include non-uniformly expanding
maps (in one or higher dimensions), maps with intermittent fixed points or
non-recurrent critical points. For a general class of examples, the compound
Poisson limit process is computed explicitly and, in particular, in the POT
case we obtain a generalised Pareto multiplicity distribution.
