Almost sure central limit theorems for the maxima of randomly chosen random variables-Reference-Cited by-同舟云学术

Almost sure central limit theorems for the maxima of randomly chosen random variables

Published:2023-04 Issue:2 Volume:63 Page:190-202
ISSN:0363-1672
Container-title:Lithuanian Mathematical Journal
language:en
Short-container-title:Lith Math J

Author:

Krajka Tomasz

Abstract

In this paper, we give an almost sure central limit theorem (ASCLT) version of a maximum limit theorem (MLT) with an arbitrary sequence {dn, n ≥ 1} of weighted means of max{Xk, k ∈ An}, where {Xn, n ≥ 1} is a sequence of independent random variables, and {An, n ≥ 1} is a sequence of almost surely finite random subsets of positive integers independent of {Xn, n ≥ 1}. Thus we generalize the cases considered in the literature: (i) the nonrandom version of ASCLT for the MLT; (ii) the version of ASCLT for randomly indexed MLT; and (iii) the version of maximum schema of observed and unobserved random variables. We complete the paper with illustrative examples.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s10986-023-09592-1.pdf

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