Conditional Strong Law of Large Numbers under G-Expectations

In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall w...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 16; no. 3; p. 272
Main Authors Zhang, Jiaqi, Tang, Yanyan, Xiong, Jie
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2024
Subjects
Brownian motion
Clusters
conditional Borel–Cantelli lemma
conditional G-capacities
conditional G-expectation
conditional strong law of large numbers
Independent variables
Mathematical analysis
Mathematical functions
Normal distribution
Probability
Probability theory
Random variables
symmetry matrix
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Summary:In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16030272