Bulletin of the
Korean Mathematical Society BKMS

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).