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ISSN 1547-7363(online) ISSN 0094-9000(print)
Strong laws of large numbers for weighted sums of $d$-dimensional arrays of random variables and applications to marked point processes
Authors:
Ta Cong Son, Tran Manh Cuong, Le Quang Dung and Le Van Dung
Journal:
Theor. Probability and Math. Statist. 111 (2024), 153-165
MSC (2020):
Primary 60B12, 60F15, 60G55, 60G60
DOI:
https://doi.org/10.1090/tpms/1220
Published electronically:
October 30, 2024
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The aim of this paper is twofold. Firstly, we give equivalent conditions for the convergence of each of three series in the Kolmogorov-type three-series theorem for random variables with multidimensional indices. Our results extend the results of Sung (2011) for multi-indexed sums. Secondly, by using these results, we develop almost sure convergence for weighted sums of $d$-dimensional arrays of random variables. We obtain the Jajte type strong law of large number for these arrays of random variables. As an application, the almost sure asymptotic behavior for sums generated by marked point processes is investigated.
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Additional Information
Ta Cong Son
Affiliation:
Department of Mathematics, Mechanics and Informatics, VNU University of Science, 334 NguyenTrai Str., Hanoi, Vietnam
Email:
congson82@gmail.com
Tran Manh Cuong
Affiliation:
Department of Mathematics, Mechanics and Informatics, VNU University of Science, 334 NguyenTrai Str., Hanoi, Vietnam
Email:
cuongtm@vnu.edu.vn
Le Quang Dung
Affiliation:
École Polytechnique, France
Email:
quangdung0110@gmail.com
Le Van Dung
Affiliation:
The University of Danang – University of Science and Education, Danang, Vietnam
Email:
lvdung@ued.udn.vn
Keywords:
Marcinkiewicz laws of large numbers,
strong laws of large numbers,
weighted sums,
multidimensional index,
marked point processes
Received by editor(s):
September 7, 2023
Accepted for publication:
December 12, 2023
Published electronically:
October 30, 2024
Additional Notes:
Tran Manh Cuong is the corresponding author.
Article copyright:
© Copyright 2024
Taras Shevchenko National University of Kyiv