| Autor: |
Zhaojun Zong, Miaomiao Gao, Feng Hu |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Results in Applied Mathematics, Vol 23, Iss , Pp 100475- (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2590-0374 |
| DOI: |
10.1016/j.rinam.2024.100475 |
| Popis: |
Motivated by some interesting problems in mathematical economics, quantum mechanics and finance, non-additive probabilities have been used to describe the phenomena which are generally non-additive. In this paper, we further study the law of the iterated logarithm (LIL) for non-additive probabilities, based on existing results. Under the framework of sublinear expectation initiated by Peng, we give two convergence results of Vn≔∑i=1nXinϕ(n) under some reasonable assumptions, where {Xi}i=1∞ is a sequence of random variables and ϕ is a positive nondecreasing function. From these, a general LIL for non-additive probabilities is proved for negatively dependent and non-identically distributed random variables. It turns out that our result is a natural extension of the Kolmogorov LIL and the Hartman–Wintner LIL. Theorem 1 and Theorem 2 in this paper can be seen an extension of Theorem 1 in Chen and Hu (2014). |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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