Precise asymptotics for a series of T. L. Lai

Spătaru, Aurel

doi:10.1090/s0002-9939-04-07524-0

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2022

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Cited by 16 publications

(2 citation statements)

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“…whenever EX=0 and EX 2 < ∞ (corresponding to the case of r = 2, p = 1 in Theorem BK). For more results on the precise rate, see Chen [1978], Spȃtaru [1999], Spȃtaru [2000a, 2000b], Spȃtaru [2004], Li and Spȃtaru [2012], etc.…”

Section: Introductionmentioning

confidence: 99%

Convergence rate in precise asymptotics for Davis law of large numbers

Kong

Dai

2016

Statistics & Probability Letters

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Let {X n , n ≥ 1} be a sequence of i.i.d. random variables with partial sums {S n , n ≥ 1}. Based on the classical Baum-Katz theorem, a paper by Heyde in 1975 initiated the precise asymptotics for the sum n≥1 P(|S n | ≥ ǫn) as ǫ goes to zero. Later, Klesov determined the convergence rate in Heyde's theorem. The aim of this paper is to extend Klesov's result to the precise asymptotics for Davis law of large numbers, a theorem in Gut and Spȃtaru [2000a].Keywords: convergence rate precise asymptotics law of large numbers MSC(2010): 60F15 60G50

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Section: Introductionmentioning

confidence: 99%

Convergence rate in precise asymptotics for Davis law of large numbers

Kong

Dai

2016

Statistics & Probability Letters

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“…whenever E[X] = 0 and E[X 2 ] < ∞. For more results on precise asymptotic problems, we refer to Chen [4], Gut and Spȃtaru [10,11], Li and Spȃtaru [20], Spȃtaru [22,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%