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Contents of PMS, Vol. 34, Fasc. 2,
pages 237 - 252
 

THE LIMITING BEHAVIOUR OF SUMS AND MAXIMUMS OF IID RANDOM VARIABLES FROM THE VIEWPOINT OF DIFFERENT OBSERVERS

Tomasz K. Krajka
Zdzisław Rychlik

Abstract: The limiting behaviour of observed and all random variables in the max limit schema was considered by Mladenović and Piterbarg (2006) and Krajka (2011). Here those results are generalised in two directions:

  • we allow more than one observer and one superobserver;
  • we consider the max limit schema as well as the sum limit schema.

2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60G70.

Keywords and phrases: Central limit theorem, extreme value theory, observed and unobserved random variables.

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