The limiting behaviour of sums and maximums of iid random variables from the viewpoint of different observers

• Autorzy: Krajka T. K. , Rychlik Z.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

central limit theorem; extreme value theory; observed random variables; unobserved random variables

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 2
• Strony: 237--252
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Krajka T. K.

• Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

autor

Rychlik Z.

• Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] P. Billingsley, Convergence of Probability Measures, Wiley, 1968.
• [2] P. Billingsley, Probability and Measure, second edition, Wiley, 1986.
• [3] T. Krajka, The asymptotic behaviour of maxima of complete and incomplete samples from stationary sequences, Stochastic Process. Appl. 121 (2011), pp. 1705-1719.
• [4] P. Mladenović and V. Piterbarg, On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences, Stochastic Process. Appl. 116 (2006), pp. 1977-1991.
• [5] V. V. Petrov, Sums of Independent Random Variables, Springer, Berlin-Heidelberg-New York 1975.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).