Asymptotics related to a series of T.L. Lai

Let {X,Xn,n≥1} be a sequence of i.i.d. random variables, and set Sn=X1+⋯+Xn. For 1<p≤3/2, if EX=0, EX2=1 and E[|X|2p(log+|X|)−p]<∞, we prove that limε↘0ε1/2∑n≥2np−2P(|Sn|≥(2p−2+ε)nlogn)=2p−1, thus extending a result by Spătaru (2004). For 1<p≤3/2 and δ>0, 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.

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Year of publication:	2012
Authors:	Li, Deli ; Spătaru, Aurel
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 8, p. 1538-1548
Publisher:	Elsevier
Subject:	Tail probabilities of sums of i.i.d. random variables \| Moderate deviations \| Lai law \| Normal distribution

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011040144