EXTREME VALUE THEORY FOR ASYMPTOTIC STATIONARYSEQUENCES
Władysław Szczotka
Abstract: The problem of behaviour of is considered when
and the sequence is asymptotically stationary in
variation.
is said to be if
where while and denote the distributions of
the sequences and respectively. The sequence of
random variables is stationary and it is said to be a stationary representation of
The main result states: under and some natural conditions
concerned and the sequence of distributions weakly
converges provided the sequence of weakly converges and the
limits are the same. An analogous result is also formulated for the processes of exceedances.