The strong law of large numbers for sums of randomly chosen random variables
نویسندگان
چکیده
Abstract Let { X n , ≥ 1} be a sequence of independent or identically distributed dependent random variables, and let A subsets natural numbers 1}. In this paper, we describe the strong law large (SLLN) form $$ {\sum}_{i\in {A}_n}\left({X}_i-\mathrm{E}{\sum}_{i\in {A}_n}{X}_i\right)/{b}_n\to 0\ \mathrm{a}.\mathrm{s}. ∑ i ∈ A n X − E / b → 0 a . s as → ∞ for some nondecreasing positive b There often arises an assumption that are almost surely increasing: ⊂ + 1 a. s 1.
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ژورنال
عنوان ژورنال: Lithuanian Mathematical Journal
سال: 2021
ISSN: ['1573-8825', '0363-1672']
DOI: https://doi.org/10.1007/s10986-021-09528-7