| Autor: |
Qingfeng Wu, Xili Tan, Shuang Guo, Peiyu Sun |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 11, Pp 29773-29805 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20241442?viewType=HTML |
| Popis: |
In this article, using the Fuk-Nagaev type inequality, we studied general strong law of large numbers for weighted sums of $ m $-widely acceptable ($ m $-WA, for short) random variables under sublinear expectation space with the integral condition $ \hat{\mathbb{E}} \left ( f^-\left ( \left | X \right | \right ) \right ) \le \mathrm{C}_\mathbb{V}\left ( f^-\left ( \left | X \right | \right ) \right )< \infty $ and $ Choquet $ integrals existence, respectively, where$ f\left ( x \right ) = x^{1/\beta }L\left ( x \right ) $for $ \beta > 1 $, $ L\left (x \right) > 0 $ $ \left(x > 0\right) $ was a monotonic nondecreasing slowly varying function, and $ f^-\left (x \right) $ was the inverse function of $ f\left(x\right) $. One of the results included the Kolmogorov-type strong law of large numbers and the partial Marcinkiewicz-type strong law of large numbers for $ m $-WA random variables under sublinear expectation space. Besides, we obtained almost surely convergence for weighted sums of $ m $-WA random variables under sublinear expectation space. These results improved the corresponding results of Ma and Wu under sublinear expectation space. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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