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One more on the convergence rates in precise asymptotics

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  • Rozovsky, L.V.

Abstract

Let ηn,n≥1, be a sequence of random variables. We study conditions under which limε↘0∑n≥1ϕ(n)P(ηn≥f(εg(n)))−ν(ε)=C,where C is a constant, assuming among other conditions that non-negative functions ϕ(x) and f(x),g(x), tend, respectively, to 0 and to ∞ as x→∞. Results obtained, in particular, are wide generalization of the similar results obtained recently in Gut and Steinebach (2013), Kong (2016), Kong and Dai (2016) and Zhang (2019).

Suggested Citation

  • Rozovsky, L.V., 2021. "One more on the convergence rates in precise asymptotics," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s0167715220303266
    DOI: 10.1016/j.spl.2020.109023
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    References listed on IDEAS

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    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.
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