Law of the single logarithm for randomly weighted sums of dependent sequences and an application

Yi Wu; Duoduo Zhao; Yi Wu; Duoduo Zhao

doi:10.3934/math.2024496

AIMS Mathematics

2024, Volume 9, Issue 4: 10141-10156. doi: 10.3934/math.2024496

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Research article

Law of the single logarithm for randomly weighted sums of dependent sequences and an application

Yi Wu ,
Duoduo Zhao ^,

School of Big Data and Artificial Intelligence, Center of Applied Mathematics, Chizhou University, Chizhou, 247000, China

Received: 22 December 2023 Revised: 04 March 2024 Accepted: 06 March 2024 Published: 14 March 2024
MSC : 60F15, 62G05

In this work, the law of the single logarithm for randomly weighted sums of widely orthant dependent random variables was studied, which improved and generalized some corresponding results in the literature. As an application, the rate of complete convergence for random weighting estimation with widely orthant dependent samples was obtained under general assumptions. Some numerical analyses were also conducted to confirm the theoretical results.
- law of the single logarithm,
- randomly weighted sums,
- complete convergence,
- random weighting estimation,
- widely orthant dependent
Citation: Yi Wu, Duoduo Zhao. Law of the single logarithm for randomly weighted sums of dependent sequences and an application[J]. AIMS Mathematics, 2024, 9(4): 10141-10156. doi: 10.3934/math.2024496

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Abstract

In this work, the law of the single logarithm for randomly weighted sums of widely orthant dependent random variables was studied, which improved and generalized some corresponding results in the literature. As an application, the rate of complete convergence for random weighting estimation with widely orthant dependent samples was obtained under general assumptions. Some numerical analyses were also conducted to confirm the theoretical results.

References

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