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Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables.
- Source :
-
Lithuanian Mathematical Journal . Jan2024, Vol. 64 Issue 1, p1-17. 17p. - Publication Year :
- 2024
-
Abstract
- Integral tests are found for the convergence of two Spitzer-type series associated with a class of weighted averages introduced by Jajte [On the strong law of large numbers, Ann. Probab., 31(1):409–412, 2003]. Our main theorems are valid for a large family of dependent random variables that are not necessarily identically distributed. As a byproduct, we improve the Marcinkiewicz–Zygmund strong law of large numbers for asymptotically almost negatively associated sequences due to Chandra and Ghosal [Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables Acta Math. Hung., 71(4):327–336, 1996]. We also complement two limit theorems recently derived by Anh et al. [TheMarcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences, J. Theor. Probab., 34(1):331–348, 2021] and Thành [On a new concept of stochastic domination and the laws of large numbers, Test, 32(1):74–106, 2023]. The obtained results are new even when the summands are independent. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LAW of large numbers
*RANDOM variables
*LIMIT theorems
*DEPENDENT variables
Subjects
Details
- Language :
- English
- ISSN :
- 03631672
- Volume :
- 64
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Lithuanian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 176452412
- Full Text :
- https://doi.org/10.1007/s10986-024-09621-7