A NOTE ON THE POINT-PROCESSES OF RARE EVENTS

We discuss the limits of point processes which are generated by a tria ngular array of rare events. Such point processes are motivated by the exceedances of a high boundary by a random sequence since exceedances are rare events in this case. This application relates the problem to extreme value theory from where the method is used to treat the asymp totic approximation of these point processes. The presented general ap proach extends, unifies and clarifies some of the various conditions u sed in the extreme value theory.