Bulletin of the Korean Mathematical Society (대한수학회보)

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ON A SPITZER-TYPE LAW OF LARGE NUMBERS FOR PARTIAL SUMS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

  • Miaomiao Wang (School of Big Data and Statistics Anhui University) ;
  • Min Wang (School of Mathematical Sciences Anhui University) ;
  • Xuejun Wang (School of Big Data and Statistics Anhui University)
  • Received : 2022.05.16
  • Accepted : 2023.01.26
  • Published : 2023.05.31
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Abstract

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 sublinear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.

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Acknowledgement

The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and for valuable suggestions which helped in improving an earlier version of this paper.

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