On a problem of a Khinchin-type decomposition theorem for extreme values
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 395-402
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Traditionally, extreme value theory has been treated in the multiplicative semigroup $\mathcal{P}$ of distribution functions (d.f's) on $\mathbf{R}^d$ endowed with the Lévy metric $L$ (which metrizes the weak convergence in $\mathcal{P}$). Unfortunately, in $(\mathcal{P},L,\cdot)$ there is no Khinchin-type decomposition theorem, as is shown in [7]. We choose another approach to extreme values, namely, we consider the multiplicative semigroup $\mathcal{F}$ of distributions on $\overline{\mathbf R}=[-\infty,\infty)^d$, introduce in it a metric $\mathcal{L}$, corresponding to the weak convergence in $\mathcal{F}$, and show that in the structure $(\mathcal{F},L,\cdot)$ there are analogues of the well known first and second Khinchin's theorems.
Keywords:
extreme values, Khinchin-type decomposition
Mots-clés : class max-$I_0$.
Mots-clés : class max-$I_0$.
@article{TVP_1994_39_2_a8,
author = {E. Pancheva},
title = {On a problem of a {Khinchin-type} decomposition theorem for extreme values},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {395--402},
publisher = {mathdoc},
volume = {39},
number = {2},
year = {1994},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a8/}
}
E. Pancheva. On a problem of a Khinchin-type decomposition theorem for extreme values. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 395-402. http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a8/