Asymptotics related to a series of T.L. Lai

Deli Li and Aurel Spătaru

Statistics & Probability Letters, 2012, vol. 82, issue 8, 1538-1548

Abstract: Let {X,Xn,n≥1} be a sequence of i.i.d. random variables, and set Sn=X1+⋯+Xn. For 10, we establish conditions for the convergence of the related series ∑n≥2np−2P(|Sn|≥(2p−2)nlogn+δn1/2loglogn(2p−2)nlogn), and derive its precise asymptotic as δ↘1/2.

Keywords: Tail probabilities of sums of i.i.d. random variables; Moderate deviations; Lai law; Normal distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.04.006

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