• East Asian mathematical journal
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• v.36 no.1
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• pp.25-34
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• 2020

The classical limit theorems like strong law of large numbers, central limit theorems and law of iterated logarithms are fundamental theories in probability and statistics. These limit theorems are proved under additivity of probabilities and expectations. In this paper, we investigate strong law of large numbers under sub-linear expectation which generalize the classical ones. We give strong law of large numbers under sub-linear expectation with respect to the partial sums and some conditions similar to Petrov's. It is an extension of the classical Chung type strong law of large numbers of Jardas et al.'s result. As an application, we obtain Chung's strong law of large number and Marcinkiewicz's strong law of large number for independent and identically distributed random variables under the sub-linear expectation. Here the sub-linear expectation and its related capacity are not additive.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.553-570
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• 2020

In this paper, we establish complete convergence for sequences of extended independent random variables and arrays of rowwise extended independent random variables under sub-linear expectations in Peng's framework. The results obtained in this paper extend the corresponding ones of Baum and Katz [1] and Hu and Taylor [11] from classical probability space to sub-linear expectation space.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.687-703
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• 2023

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.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1485-1508
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• 2020

In this paper, we investigate the complete f-moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete f-moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.

• Journal of the Korean Applied Science and Technology
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• v.38 no.6
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• pp.1445-1454
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• 2021

In this study, based on the expectation that beauty education based on VR experience of beauty majors will have on expertise and practical ability, it was attempted to develop VR-based beauty subjects and secure an educational environment. A total of 106 learners participated in the study, and the online questionnaire consisted of questions about the development of VR-based beauty subjects, recognition of expertisee and practical skills, and general characteristics. The collected data were verified at the significance level of .05 using the SPSS 21.0 statistical program. As a result of frequency analysis, factor analysis, correlation, and linear regression analysis, the higher the grade, the higher the perception of VR-based beauty subjects development (p<.01). The perception of VR-based beauty subject development was related to VR-based expertise and practical skills for each sub-factor of the recognition of expertise (r=.683, p<.001), practical skills (r=.676, p<.001), and industry-related awareness (r=.543, p<.001). It was found that there was a statistically significant positive (+) correlation with related perception. In addition, it was found that the higher the awareness of VR-based beauty subjects development, the higher the expectation that expertise, practical ability, and industry-related awareness would be improved. As a result, the necessity of developing VR-based beauty subjects and expectations for course operation of majors in the beauty subjects environment were confirmed. In follow-up studies, it is necessary to expand the scope of the sample.