Max-semistability: a survey

Abstract. In the classical limit theory for normalized sums of independent random variables we change the operation ”sum” by the operation “maximum”. How does it change the classical structure of the limit probability laws? The max-model enriches Probability Theory with interesting non-classical phenomena. Several of them will be discussed here. As an example for characterizing a limit class of probability distributions we consider the class of maxsemistable df’s. It is interesting to observe that the max-semistability property is a characteristic property of the univariate distributions of semi-selfsimilar extremal processes with stationary max-increments. Mathematics Subject Classification. 62E20 ; 60G51 .