Regularly varying functions. (English) Zbl 1164.60301

Jessen, Anders Hedegaard; Mikosch, Thomas

Publ. Inst. Math., Nouv. Sér. 80(94), 171-192 (2006).

The authors review some known results on basic functions acting on regularly varying random variables and random vectors such as sums, products, linear combinations, maxima and minima and powers. These results are useful in applications related to time series analysis, risk management, insurance and telecommunications. Most of the results belong to the folklore but they are often wide spread over the literature and not always easily accessible. The authors also provide a list of 57 references on the subject.

Reviewer: Pavle Mladenović (Beograd)

MSC:

60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60G70	Extreme value theory; extremal stochastic processes
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

regular variation; sums and products; linear combinations; maxima and minima