Geodesic
On maximum domain of attraction for transformations of normal random variable
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 207-215 
V. V. Troshin. On maximum domain of attraction for transformations of normal random variable. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 207-215. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Limit distributions of the maximum of independent copies of a transformation of a Gaussian random variable are studied. Sufficient and necessary conditions are found for the transformations belonging to Fréchet and Weibull maximum domains of attraction. Simple sufficient conditions are also given.

[1] Piterbarg V. I., Mazur A. E., “Gaussovskie kopulnye vremennye ryady s tyazhelymi khvostami i silnoi vremennoi zavisimostyu”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 60:5 (2015), 3–7

[2] De Haan L., Ferreira A., Extreme Value Theory: An Introduction, Springer, New York, 2007 | MR

[3] Piterbarg V. I., Asymptotic Methods in Theory of Gaussian Random Processes and Fields, Transl. Math. Monogr., 148, Amer. Math. Soc., Providence, 2012 | DOI | MR

[4] Seneta E., Regularly Varying Functions, Lect. Notes Math., 508, Springer, Berlin, 1976 | DOI | MR | Zbl