Bull. Korean Math. Soc. 2023; 60(3): 687-703
Online first article March 27, 2023 Printed May 31, 2023
https://doi.org/10.4134/BKMS.b220341
Copyright © The Korean Mathematical Society.
Miaomiao Wang, Min Wang, Xuejun Wang
Anhui University; Anhui University; Anhui University
In this paper, under some suitable conditions, we study the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables in upper expectation space. Some general results on necessary and sufficient conditions of the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables under sub-linear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.
Keywords: Independent and identically distributed random variables, law of large numbers, complete convergence, sub-linear expectation space, capacity
MSC numbers: 60F15
Supported by: Supported by the National Natural Science Foundation of China (11871072, 12201079, 12201600), the Natural Science Foundation of Anhui Province (2108085MA06), and the Scientific Research Project of Graduate Students in Anhui Universities (YJS20210077).
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