The paper studies moderate deviation principles in weighted sums of independent random variables, indicating their applications in time series and branching processes.
In the present paper, we consider the weighted sums of sums of independent and identically distributed random variables and study their moderate deviation principles, which can be applied to study the asymptotic behavior of time series and branching processes. These results can be seen as the complements of the results in Imomov and Nazarov [6].
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Du et al. (2025) studied this question.
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