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Asymptotics related to a series of T.L. Lai

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  • Li, Deli
  • Spătaru, Aurel

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.

Suggested Citation

  • Li, Deli & Spătaru, Aurel, 2012. "Asymptotics related to a series of T.L. Lai," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1538-1548.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1538-1548
    DOI: 10.1016/j.spl.2012.04.006
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    Cited by:

    1. Kong, Lingtao & Dai, Hongshuai, 2016. "Convergence rate in precise asymptotics for Davis law of large numbers," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 295-300.
    2. Francisco Azuero & Jorge Armando Rodríguez, 2016. "Preservación ambiental de la Amazonia colombiana: retos para la política fiscal," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 35(Especial ), pages 281-313, January.

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