Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications

In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz’s...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 35; no. 2; pp. 172 - 184
Main Authors Xu, Jia Pan, Zhang, Li Xin
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.02.2019
Springer Nature B.V
Subjects
Independent variables
Mathematics
Mathematics and Statistics
Random variables
Theorems
Sub-linear expectation
Marcinkiewicz’s strong law of large numbers
Kolmogorov’s three series theorem
Rosenthal’s inequality
capacity
60F15
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Summary:In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz’s strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-018-7508-9